Worksheet on Proportions will guide the students to learn the complete concept of proportions. Proportions Worksheet includes different problems with answers. Practice all problems and improve your preparation level easily. We have included objective questions and practice tests to provide you with the best preparation resources. Check your knowledge by taking help from the free Worksheet on Proportion from our website.<\/p>\n
Be the first one to learn the Proportions concept using the Simple Worksheet on Proportions. Students can easily score good marks in the exam by practicing all questions available here.<\/p>\n
1. Check if each of the following is in proportion. (a) Given numbers are 12, 42, 24, 8. Therefore, the given numbers 12, 42, 24, 8 are not in proportion.<\/p>\n (b) Given numbers are 8, 6, 12, 90. Therefore, the given numbers 8, 6, 12, 90 are not in proportion.<\/p>\n (c) Given numbers are 10, 16, 400, 250. Therefore, the given numbers 10, 16, 400, 250 are not in proportion.<\/p>\n (d) Given numbers are 60, 32, 90, 50. Therefore, the given numbers 60, 32, 90, 50 are not in proportion.<\/p>\n (e) Given numbers are 36, 16, 108, 48. Therefore, the given numbers 36, 16, 108, 48 are in proportion.<\/p>\n (f) Given numbers are 12, 16, 48, 60. Therefore, the given numbers 12, 16, 48, 60 are not in proportion.<\/p>\n<\/details>\n 2. Find the value of x in the following? (a) Given ratios are 12 : 18 :: 2x : 30. Therefore, the value of x is 10.<\/p>\n (b) Given ratios are x : 7 :: 12 : 21. Therefore, the value of x is 4.<\/p>\n (c) Given ratios are 2 : 2x :: 16 : 28. Therefore, the value of x is 1.75.<\/p>\n (d) Given ratios are 3x : 9 :: 1.2 : 1.5. Therefore, the value of x is 2.4.<\/p>\n (e) Given ratios are 2\/3 \u2236 2\/4 : : 2\/9 : 2x. Therefore, the value of x is \\(\\frac { 1 }{ 12 } \\).<\/p>\n (f) Given ratios are 8 : x :: 4 : 10. Therefore, the value of x is 20.<\/p>\n (g) Given ratios are 4 : 14 :: 2x : 84. Therefore, the value of x is 12.<\/p>\n (h) Given ratios are 3 : 2 :: 3 : x. Therefore, the value of x is 2.<\/p>\n (i) Given ratios are 2x : 3 :: 12.6 : 9. Therefore, the value of x is 2.1.<\/p>\n<\/details>\n 3. Find the fourth proportional to (a) Given numbers are 36, 108, 12. Therefore, the fourth proportional is 36.<\/p>\n (b) Given numbers are 60, 64, 84. Therefore, the fourth proportional is 89.6.<\/p>\n (c) Given numbers are 8, 6, 12. Therefore, the fourth proportional is 9.<\/p>\n (d) Given numbers are 4, 12, 2. Therefore, the fourth proportional is 6.<\/p>\n (e) Given numbers are 64, 48, 16. Therefore, the fourth proportional is 12.<\/p>\n<\/details>\n 4. Find the third proportional to (a) Given numbers are 4, and 8. Therefore, the third proportional is 16.<\/p>\n (b) Given numbers are 6, and 18. Therefore, the third proportional is 54.<\/p>\n (c) Given numbers are 72, and 84. Therefore, the third proportional is 98.<\/p>\n (d) Given numbers are 32, and 72. Therefore, the third proportional is 162.<\/p>\n (e) Given numbers are 28, and 56. Therefore, the third proportional is 112.<\/p>\n (f) Given numbers are 96, and 192. Therefore, the third proportional is 384.<\/p>\n<\/details>\n 5. Find the mean proportional between (a) Given numbers are 72 and 8. Therefore, the mean proportional is 24.<\/p>\n (b) Given numbers are 2.4 and 0.6. Therefore, the mean proportional is 1.2.<\/p>\n (c) Given numbers are 50 and 18. Therefore, the mean proportional is 30.<\/p>\n (d) Given numbers are 48 and 108. Therefore, the mean proportional is 72.<\/p>\n (e) Given numbers are 2\/9 and 8. Therefore, the mean proportional is 4\/3.<\/p>\n<\/details>\n 6. The first, second, and fourth terms of the proportion are 18, 42, 154. Find the third term.<\/p>\n Given that the first, second, and fourth terms of the proportion are 18, 42, 154. Therefore, the third term is 66.<\/p>\n<\/details>\n 7. The second, third, and fourth terns of the proportion are 54, 70, 126. Find the first term.<\/p>\n Given that the second, third, and fourth terns of the proportion are 54, 70, 126. Therefore, the first term is 30.<\/p>\n<\/details>\n 8. In the school library, the ratio of maths books to science studies books is the same as the ratio of science studies books to English books. If there are 900 books in maths and 600 books in science studies, find the number of books in English?<\/p>\n Given that In the school library, the ratio of maths books to science studies books is the same as the ratio of science studies books to English books. Therefore, the number of books in English is 400.<\/p>\n<\/details>\n 9. If 8 books cost $56, what will the cost of 40 books be?<\/p>\n Given that 8 books cost $56. Therefore, the cost of 40 books is $280.<\/p>\n<\/details>\n 10. The ratio of length and breadth of a playground is 6 : 4. Find the length if breadth is 72 m.<\/p>\n Given that the ratio of length and breadth of a playground is 6 : 4. Therefore, the length is 108m.<\/p>\n<\/details>\n","protected":false},"excerpt":{"rendered":" Worksheet on Proportions will guide the students to learn the complete concept of proportions. Proportions Worksheet includes different problems with answers. Practice all problems and improve your preparation level easily. We have included objective questions and practice tests to provide you with the best preparation resources. 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\n(a) 12, 42, 24, 8
\n(b) 8, 6, 12, 90
\n(c) 10, 16, 400, 250
\n(d) 60, 32, 90, 50
\n(e) 36, 16, 108, 48
\n(f) 12, 16, 48, 60<\/p>\nSolution:<\/summary>\n
\nFrom the given data, extreme terms are 12 and 8, mean terms are 42 and 24.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 12 \u00d7 8 = 96
\nProduct of mean terms = 42 \u00d7 24 = 1008.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n96 is not equal to 1008.<\/p>\n
\nFrom the given data, extreme terms are 8 and 90, mean terms are 6 and 12.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 8 \u00d7 90 = 720
\nProduct of mean terms = 6 \u00d7 12 = 72.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n720 is not equal to 72.<\/p>\n
\nFrom the given data, extreme terms are 10 and 250, mean terms are 16 and 400.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 10 \u00d7 250 = 2500
\nProduct of mean terms = 16 \u00d7 400 = 6400.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n2500 is not equal to 6400.<\/p>\n
\nFrom the given data, extreme terms are 60 and 50, mean terms are 32 and 90.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 60 \u00d7 50 = 3000
\nProduct of mean terms = 32 \u00d7 90 = 2880.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n3000 is not equal to 2880.<\/p>\n
\nFrom the given data, extreme terms are 36 and 48, mean terms are 16 and 108.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 36 \u00d7 48 = 1728
\nProduct of mean terms = 16 \u00d7 108 = 1728.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n1728 is not equal to 1728.<\/p>\n
\nFrom the given data, extreme terms are 12 and 60, mean terms are 16 and 48.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 12 \u00d7 60 = 720
\nProduct of mean terms = 16 \u00d7 48 = 768.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n720 is not equal to 768.<\/p>\n
\n
\n(a) 12 : 18 :: 2x : 30
\n(b) x : 7 :: 12 : 21
\n(c) 2 : 2x :: 16 : 28
\n(d) 3x : 9 :: 1.2 : 1.5
\n(e) 2\/3 \u2236 2\/4 : : 2\/9 : 2x
\n(f) 8 : x :: 4 : 10
\n(g) 4 : 14 :: 2x : 84
\n(h) 3 : 2 :: 3 : x
\n(i) 2x : 3 :: 12.6 : 9<\/p>\nSolution:<\/summary>\n
\nWe need to find the value of x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 12 and 30, mean terms are 18 and 2x.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 12 \u00d7 30 = 360
\nProduct of mean terms = 18 \u00d7 2x = 36x.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n36x = 360
\nx = \\(\\frac { 360 }{ 36 } \\)
\nx = 10<\/p>\n
\nWe need to find the value of x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are x and 21, mean terms are 7 and 12.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 21 \u00d7 x = 21x
\nProduct of mean terms = 7 \u00d7 12 = 84.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n21x = 84
\nx = \\(\\frac { 84 }{ 21 } \\)
\nx = 4<\/p>\n
\nWe need to find the value of x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 2 and 28, mean terms are 2x and 16.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 2 \u00d7 28 = 56
\nProduct of mean terms = 2x \u00d7 16 = 32x.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n32x = 56
\nx = \\(\\frac { 56 }{ 32 } \\)
\nx = 1.75<\/p>\n
\nWe need to find the value of x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 3x and 1.5, mean terms are 9 and 1.2.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 3x \u00d7 1.5 = 4.5x
\nProduct of mean terms = 9 \u00d7 1.2 = 10.8.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n4.5x = 10.8
\nx = \\(\\frac { 10.8 }{ 4.5 } \\)
\nx = 2.4<\/p>\n
\nWe need to find the value of x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 2\/3 and 2x, mean terms are 2\/4 and 2\/9.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 2\/3 \u00d7 2x = 4\/3x
\nProduct of mean terms = 2\/4 \u00d7 2\/9 = 1\/9.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n4\/3x = 1\/9
\nx = \\(\\frac { 1\/9 }{ 4\/3 } \\)
\nx = \\(\\frac { 1 }{ 12 } \\)<\/p>\n
\nWe need to find the value of x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 8 and 10, mean terms are x and 4.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 8 \u00d7 10 = 80
\nProduct of mean terms = x \u00d7 4 = 4x.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n4x = 80
\nx = \\(\\frac { 80 }{ 4 } \\)
\nx = 20<\/p>\n
\nWe need to find the value of x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 4 and 84, mean terms are 14 and 2x.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 4 \u00d7 84 = 336
\nProduct of mean terms = 14 \u00d7 2x = 28x.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n28x = 336
\nx = \\(\\frac { 336 }{ 28 } \\)
\nx = 12<\/p>\n
\nWe need to find the value of x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 3 and x, mean terms are 2 and 3.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 3 \u00d7 x = 3x
\nProduct of mean terms = 2 \u00d7 3 = 6.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n3x = 6
\nx = \\(\\frac { 6 }{ 3 } \\)
\nx = 2<\/p>\n
\nWe need to find the value of x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 2x and 9, mean terms are 3 and 12.6.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 2x \u00d7 9 = 18x
\nProduct of mean terms = 3 \u00d7 12.6 = 37.8.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n18x = 37.8
\nx = \\(\\frac { 37.8 }{ 18 } \\)
\nx = 2.1<\/p>\n
\n
\n(a) 36, 108, 12
\n(b) 60, 64, 84
\n(c) 8, 6, 12
\n(d) 4, 12, 2
\n(e) 64, 48, 16<\/p>\nSolution:<\/summary>\n
\nLet the fourth proportional to 36, 108, 12 be x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 36 and x, mean terms are 108 and 12.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 36 \u00d7 x = 36x
\nProduct of mean terms = 108 \u00d7 12 = 1296.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n36x = 1296
\nx = \\(\\frac { 1296 }{ 36 } \\)
\nx = 36<\/p>\n
\nLet the fourth proportional to 60, 64, 84 be x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 60 and x, mean terms are 64 and 84.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 60 \u00d7 x = 60x
\nProduct of mean terms = 64 \u00d7 84 = 5376.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n60x = 5376
\nx = \\(\\frac { 5376 }{ 60 } \\)
\nx = 89.6<\/p>\n
\nLet the fourth proportional to 8, 6, 12 be x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 8 and x, mean terms are 6 and 12.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 8 \u00d7 x = 8x
\nProduct of mean terms = 6 \u00d7 12 = 72.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n8x = 72
\nx = \\(\\frac { 72 }{ 8 } \\)
\nx = 9<\/p>\n
\nLet the fourth proportional to 4, 12, 2 be x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 4 and x, mean terms are 12 and 2.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 4 \u00d7 x = 4x
\nProduct of mean terms = 12 \u00d7 2 = 24.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n4x = 24
\nx = \\(\\frac { 24 }{ 4 } \\)
\nx = 6<\/p>\n
\nLet the fourth proportional to 64, 48, 16 be x.
\nThe four numbers are in proportion.
\nTherefore, The product of means = product of extremes
\nFrom the given data, extreme terms are 64 and x, mean terms are 48 and 16.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 64 \u00d7 x = 64x
\nProduct of mean terms = 48 \u00d7 16 = 768.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n64x = 768
\nx = \\(\\frac { 768 }{ 64 } \\)
\nx = 12<\/p>\n
\n
\n(a) 4, 8
\n(b) 6, 18
\n(c) 72, 84
\n(d) 32, 72
\n(e) 28, 56
\n(f) 96, 192<\/p>\nSolution:<\/summary>\n
\nLet the third proportional to 4, and 8 be x.
\nThe three numbers are in proportion.
\nTherefore, the square of middle term = multiplication of first and last term.
\nb\u00b2 = ac
\nFrom the given data, the middle term is 8, first and the last terms are 4 and x.
\nFind the square of the middle term and the product of the first and last term.
\nSquare of the middle term = 8\u00b2 = 8 \u00d7 8 = 64
\nProduct of first and last term = 4 \u00d7 x = 4x.
\nCompare the Square of the middle term and Product of the first and last term.
\nSquare of the middle term = Product of the first and last term
\n64 = 4x
\nx = \\(\\frac { 64 }{ 4 } \\)
\nx = 16<\/p>\n
\nLet the third proportional to 6, and 18 be x.
\nThe three numbers are in proportion.
\nTherefore, the square of middle term = multiplication of first and last term.
\nb\u00b2 = ac
\nFrom the given data, the middle term is 18, first and the last terms are 6 and x.
\nFind the square of the middle term and the product of the first and last term.
\nSquare of the middle term = 18\u00b2 = 18 \u00d7 18 = 324
\nProduct of first and last term = 6 \u00d7 x = 6x.
\nCompare the Square of the middle term and Product of the first and last term.
\nSquare of the middle term = Product of the first and last term
\n324 = 6x
\nx = \\(\\frac { 324 }{ 6 } \\)
\nx = 54<\/p>\n
\nLet the third proportional to 72, and 84 be x.
\nThe three numbers are in proportion.
\nTherefore, the square of middle term = multiplication of first and last term.
\nb\u00b2 = ac
\nFrom the given data, the middle term is 48, first and the last terms are 72 and x.
\nFind the square of the middle term and the product of the first and last term.
\nSquare of the middle term = 84\u00b2 = 84 \u00d7 84 = 7056
\nProduct of first and last term = 72 \u00d7 x = 72x.
\nCompare the Square of the middle term and Product of the first and last term.
\nSquare of the middle term = Product of the first and last term
\n7056 = 72x
\nx = \\(\\frac { 7056 }{ 72 } \\)
\nx = 98<\/p>\n
\nLet the third proportional to 32, and 72 be x.
\nThe three numbers are in proportion.
\nTherefore, the square of middle term = multiplication of first and last term.
\nb\u00b2 = ac
\nFrom the given data, the middle term is 72, first and the last terms are 32 and x.
\nFind the square of the middle term and the product of the first and last term.
\nSquare of the middle term = 72\u00b2 = 72 \u00d7 72 = 5184
\nProduct of first and last term = 32 \u00d7 x = 32x.
\nCompare the Square of the middle term and Product of the first and last term.
\nSquare of the middle term = Product of the first and last term
\n5184 = 32x
\nx = \\(\\frac { 5184 }{ 32 } \\)
\nx = 162<\/p>\n
\nLet the third proportional to 28, and 56 be x.
\nThe three numbers are in proportion.
\nTherefore, the square of middle term = multiplication of first and last term.
\nb\u00b2 = ac
\nFrom the given data, the middle term is 56, first and the last terms are 28 and x.
\nFind the square of the middle term and the product of the first and last term.
\nSquare of the middle term = 56\u00b2 = 56 \u00d7 56 = 3136
\nProduct of first and last term = 28 \u00d7 x = 28x.
\nCompare the Square of the middle term and Product of the first and last term.
\nSquare of the middle term = Product of the first and last term
\n3136 = 28x
\nx = \\(\\frac { 3136 }{ 28 } \\)
\nx = 112<\/p>\n
\nLet the third proportional to 96, and 192 be x.
\nThe three numbers are in proportion.
\nTherefore, the square of middle term = multiplication of first and last term.
\nb\u00b2 = ac
\nFrom the given data, the middle term is 192, first and the last terms are 96 and x.
\nFind the square of the middle term and the product of the first and last term.
\nSquare of the middle term = (192)\u00b2 = 192 \u00d7 192 = 36864
\nProduct of first and last term = 96 \u00d7 x = 96x.
\nCompare the Square of the middle term and Product of the first and last term.
\nSquare of the middle term = Product of the first and last term
\n36864 = 96x
\nx = \\(\\frac { 36864 }{ 96 } \\)
\nx = 384<\/p>\n
\n
\n(a) 72 and 8
\n(b) 2.4 and 0.6
\n(c) 50 and 18
\n(d) 48 and 108
\n(e) 2\/9 and 8<\/p>\nSolution:<\/summary>\n
\nLet the mean proportional to 72 and 8 be x.
\nThe three numbers are in proportion.
\nTherefore, the square of middle term = multiplication of first and last term.
\nb\u00b2 = ac
\nFrom the given data, the middle term is x, first and the last terms are 72 and 8.
\nFind the square of the middle term and the product of the first and last term.
\nSquare of the middle term = x\u00b2
\nProduct of first and last term = 72 \u00d7 8 = 576.
\nCompare the Square of the middle term and Product of the first and last term.
\nSquare of the middle term = Product of the first and last term
\n576 = x\u00b2
\nx = \u221a576
\nx = 24<\/p>\n
\nLet the mean proportional to 2.4 and 0.6.
\nThe three numbers are in proportion.
\nTherefore, the square of middle term = multiplication of first and last term.
\nb\u00b2 = ac
\nFrom the given data, the middle term is x, first and the last terms are 2.4 and 0.6.
\nFind the square of the middle term and the product of the first and last term.
\nSquare of the middle term = x\u00b2
\nProduct of first and last term = 2.4 \u00d7 0.6 = 1.44.
\nCompare the Square of the middle term and Product of the first and last term.
\nSquare of the middle term = Product of the first and last term
\n1.44 = x\u00b2
\nx = \u221a1.44
\nx = 1.2<\/p>\n
\nLet the mean proportional to 50 and 18 be x.
\nThe three numbers are in proportion.
\nTherefore, the square of middle term = multiplication of first and last term.
\nb\u00b2 = ac
\nFrom the given data, the middle term is x, first and the last terms are 50 and 18.
\nFind the square of the middle term and the product of the first and last term.
\nSquare of the middle term = x\u00b2
\nProduct of first and last term = 50 \u00d7 18 = 900.
\nCompare the Square of the middle term and Product of the first and last term.
\nSquare of the middle term = Product of the first and last term
\n900 = x\u00b2
\nx = \u221a900
\nx = 30<\/p>\n
\nLet the mean proportional to 48 and 108 be x.
\nThe three numbers are in proportion.
\nTherefore, the square of middle term = multiplication of first and last term.
\nb\u00b2 = ac
\nFrom the given data, the middle term is x, first and the last terms are 48 and 108.
\nFind the square of the middle term and the product of the first and last term.
\nSquare of the middle term = x\u00b2
\nProduct of first and last term = 48 \u00d7 108 = 5184.
\nCompare the Square of the middle term and Product of the first and last term.
\nSquare of the middle term = Product of the first and last term
\n5184 = x\u00b2
\nx = \u221a5184
\nx = 72<\/p>\n
\nLet the mean proportional to 2\/9 and 8 be x.
\nThe three numbers are in proportion.
\nTherefore, the square of middle term = multiplication of first and last term.
\nb\u00b2 = ac
\nFrom the given data, the middle term is x, first and the last terms are 2\/9 and 8.
\nFind the square of the middle term and the product of the first and last term.
\nSquare of the middle term = x\u00b2
\nProduct of first and last term = 2\/9 \u00d7 8 = 16\/9.
\nCompare the Square of the middle term and Product of the first and last term.
\nSquare of the middle term = Product of the first and last term
\n16\/9 = x\u00b2
\nx = \u221a(16\/9)
\nx = 4\/3<\/p>\n
\nSolution:<\/summary>\n
\nLet the third term be x.
\nFrom the given data, extreme terms are 18 and 154, mean terms are 42 and x.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = 18 \u00d7 154 = 2772
\nProduct of mean terms = 42 \u00d7 x = 42x.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n42x = 2772
\nx = \\(\\frac { 2772 }{ 42 } \\)
\nx = 66.<\/p>\n
\nSolution:<\/summary>\n
\nLet the first term be x.
\nFrom the given data, extreme terms are x and 126, mean terms are 54 and 70.
\nFind the Product of extreme terms and mean terms.
\nProduct of extreme terms = x \u00d7 126 = 126x
\nProduct of mean terms = 54 \u00d7 70 = 3780.
\nCompare the Product of extreme terms and the Product of mean terms.
\nThe product of means = product of extremes
\n126x = 3780
\nx = \\(\\frac { 3780 }{ 126 } \\)
\nx = 30.<\/p>\n
\nSolution:<\/summary>\n
\nThere are 900 books in maths and 600 books in science studies.
\nThe ratio of maths and science studies books = 900 : 600 = 3 : 2
\nLet the English books be x.
\nThe ratio of science studies books to English books = 600 : x.
\nGiven the ratio of maths books to science studies books is the same as the ratio of science studies books to English books.
\nTherefore, 3 : 2 = 600 : x
\n3x = 1200
\nx = \\(\\frac { 1200 }{ 3 } \\)
\nx = 400.<\/p>\n
\nSolution:<\/summary>\n
\nFind one book’s cost from the above information.
\n1 book cost = $56\/8 = $7.
\nNow, find the cost of 40 books.
\nTo find the cost of 40 books, multiply 40 books by $7.
\nThe cost of 40 books = 40 \u00d7 $7 = $280.<\/p>\n
\nSolution:<\/summary>\n
\nThe breadth is 72 m
\nlength : breadth = 6 : 4
\nlength : 72m = 6 : 4
\nThe length = \\(\\frac { 6 }{ 4 } \\) \u00d7 72m
\nThe length = 108m<\/p>\n