Unitary Method is all about finding the value of a single unit. Here in this article, we have covered Problems on Unitary Method using Direct Variation. Refer to them and try to solve on your own and then cross-check with the solutions provided to assess your preparation standards. Unitary Method using Direct Variation Questions with Solutions PDF can be quite handy to finish your homework or clear your queries after the class. Solve different types of problems on direct variation using unitary method and become proficient in the concept.
Do Refer:
- Word Problems on Unitary Method
- Worksheet on Unitary Method
- Worksheet on Direct Variation using Unitary Method
Unitary Method Direct Variation Sums
I. If 4 men and 2 women can earn Rs 320 in a day, find how much 6 men and 12 women will earn in a day?
Solution:
This is a situation of direct variation.
More men can earn more in a day.
In a day 4 men can earn money= Rs 320
1 man can earn =Rs 320/4 and
6 men can earn Rs 320/4 × 6 = Rs 480
Also, 2 women can earn Rs 320 and
1 woman can earn Rs 320/2 = Rs 160
12 women can earn = Rs 160 × 12 = Rs 1920
Therefore, 6 men and 12 women can earn Rs(480 + 1920) = Rs 2400.
II. A labour gets Rs 900 for 12 days of work. How many days should he work to get Rs 2400?
Solution:
This is also a situation of direct variation as money is received for working more days.
Rs 900 is earned by labour in 12 days.
Rs 1 is earned by labour in 12/900 days.
Rs2400 is earned by labour in 12/900 × 2400 days=30
Therefore, Rs 2100 is earned by labour in 30 days.
III. If Ajay saves 960 Rs in 12 days, how much amount will he save in 25 days?
Solution:
Given that,
Ajay saves money in 12 days=Rs 960
Saving of Ajay in 1 day=960/12
=80 Rs
Saving of Ajay in 25 days=80 × 25 =2000 Rs
Therefore, Ajay saves Rs 2000 in 25 days.
IV. 350 apples can be placed in 25 cartoons. How many apples can be placed in 16 cartoons?
Solution:
Given that,
No.of apples placed in 25 cartoons is 350
No.of apples can be placed in 1 cartoon =350/25
=14 apples
Hence, No. of apples can be placed in 16 cartoons =16 × 14= 224 apples.
V. In a business, if A can earn Rs 8000 in 2 years, At the same rate, find his earning for 5 years.
Solution :
This is a situation of direct variation.
Because more time —–> more earning
Given that,
Earning for 2 years is Rs 8000
Earning for 1 year is
= 8000 / 2
= Rs4000
Then, earning for 5 years is
= 5 ⋅ 4000
= Rs 20,000
So, the earning for 5 years is Rs 20,000.
VI. Rakesh would like to hire a call taxi for 700 miles trip. If the cost of the taxi is Rs 5.50 per mile, what is the total cost for his trip?
Solution:
This is a situation of direct variation.
Because
more miles —–> more cost
Given that,
Cost for one mile = Rs 5.50
The cost of 300 miles is
= 5.50 ⋅ 300
= Rs 1650
Hence, the total cost for the trip is Rs 1650.
VII. Janci ordered 500 gm of ghee for Rs 495. Then she reduced her order to 280 units. How much money does Janci have to pay for 280 units?
Solution:
This is a situation of direct variation.
Because fewer units —–> less cost
Cost of 500 gm = Rs 495
The cost of 1 unit is
= 495 / 500
= 0.99
The cost of 280 units is
= 0.99 ⋅ 280
= Rs 277
So, Janci has to pay Rs 277 for 280 units.
VIII. If Dev sells 2 litres of juice for Rs 40, how much money will he earn by selling 70 litres of juice?
Solution :
This is a situation of direct variation. Because
more gallons of juice —–> amount received will be more
Given that, 2 litres of juice cost Rs 40
The cost of one gallon of juice is= 40 / 2
= Rs 20
The Cost of 70 litres of juice is
= 70 ⋅ 20
= Rs 1400
Hence, Dev will earn Rs1400 by selling 70 litres of juice.
IX. In 3 days, Sarath raised Rs 2,379 for cancer research. How much money will he raise in 20 days?
Solution:
This is a situation of direct variation. Because
more number of weeks —-> amount raised will be more
Given that, Sarath raised Rs 2,379 in 20 days
Amount raised in one day is
= 2379 / 3
= Rs 793
Amount raised in 20 days is= 793 ⋅ 20
= Rs 15860
Hence, the money raised in 20 weeks is Rs15860.
X. Ramya can type 690 words in 30 minutes. How many words will she be able to type in 10 minutes with the same efficiency?
Solution:
The number of words typed in 30min=690.
The number of words typed in 1min=690/30=23
Therefore, the number of words typed in 10min=10×23=230.
Hence, Ramya will be able to type 230 words in 10 minutes.
XI. 75 plastic boxes cost Rs 3,750. Find the cost of 24 such plastic boxes?
Solution:
This is a situation of direct variation.
Because
less number of plastic boxes —–> cost will be less
Given that, 75 plastic boxes cost Rs 3,750
The cost of one plastic box is
= 3750 / 75
= Rs 50
Then, the cost of 24 plastic boxes is
= 24 ⋅ 50
= Rs 1200
Therefore, the cost of 24 plastic boxes is Rs 1200.
XII. 20 m of cloth costs Rs 900. Find the cost of 65 m of the same cloth?
Solution:
Given that,
The cost for 20 m of cloth is= Rs 900
The cost for 1 m of cloth is =900/20
=45 Rs
Thus, the cost for 65 m of cloth =65 × 45= Rs 2925