Practice the questions in the Worksheet on Direct Variation using Unitary Method and learn the concept on a deeper level. Solve the different types of problems based on the Unitary Method and know the approach used. Test your knowledge on the concept of Unitary Method using Direct Variation by solving the problems available in the Unitary Method Direct Variation Worksheet. Simply try to answer them on your own and then cross-check with the solutions provided to improve on the areas accordingly.
Worksheet on Unitary Method using Direct Variation
I. In a toy shop, 20 toys cost Rs. 1,330.50. Find the cost of 16 toys?
Solution:
Given,
Cost of 20 toys=Rs 1,330.50
Cost of 1 toy=Rs 1,330.50/20
=66.525
The cost of 16 toys=66.525 × 16
=1064.4
Hence, the cost of 16 toys is Rs 1064.4.
II. In a business, if Arjun can earn Rs 4,75,000 in 2.5 years, At the same rate, find his earning for 4 years?
Solution:
Given,
Arjun can earn money in 2.5 years=Rs 4,75,000
Earning money for 1 year is=Rs 4,75,000/2.5
=Rs 190000
Earning money for 4 year is=190000 × 4
=Rs 760000
Therefore, Arjun earns money for 4 years is Rs 760000.
III. Sunil gets Rs 500 for 7 hours of work. How much money does he get for 3 hours?
Solution:
Given,
Sunil gets money for 7 hours of work=Rs 500
Sunil gets money for 1 hour of work=Rs 500/7=Rs 71.42
Sunil gets money for 3 hours of work= Rs 71.42 × 3
=Rs 214.26
Hence, Sunil gets money for 3 hours is Rs 214.26.
Iv. Sanjana would like to buy 10 dresses. If the cost of each dress is Rs 700, what is the total cost for 10 dresses?
Solution:
Given,
The cost of each dress is =Rs 700
The total cost for 10 dresses=Rs 700 × 10
=Rs 7000
Therefore, the total cost of 10 dresses is Rs 7000.
V. Gopal bought a dozen apples for Rs 500. Find the cost of 15 such apples. How many apples can be bought for Rs 83.32?
Solution:
Given,
Gopal bought a dozen apples for= Rs 500
Cost of 1 apple=Rs 500/12=Rs 41.66
Cost of 15 such apples=15 × 41.66=624.9
No. of apples can be bought for Rs 83.32=83.32/41.66=2
Hence, Gopal can buy two apples for Rs 83.32.
VI. The weight of 50 Handbags is 6 kg.
(a) What is the weight of 80 such Handbags?
(b) How many such Handbags weigh 7.5 Kg?
Solution:
Given,
The weight of 50 Handbags is =6 kg
The weight of 1 handbag is=6/50=0.12
The weight of 80 such Handbags=80 × 0.12=9.6
No. of Handbags weigh 7.5 Kg=7.5/0.12=62.5
Hence, No. of handbags weigh 7.5 kg is 62.5 handbags.
VII. In 5 weeks, Mahesh raised the fund of Rs 25,539.50 for helping the poor people. How much money will he raise in 20 weeks?
Solution:
Given,
Mahesh raised the money for helping the poor people in 5 weeks=Rs 25,539.50
Mahesh raised the money in one week= Rs 25,539.50/5=5107.9
Mahesh will raise money in 20 weeks=20 × 5107.9=102158
Hence, Mahesh will raise money in 20 weeks is Rs 102158.
VIII. Janci ordered 5liters of oil for Rs 550. Then she reduced her order to 3 liters. How much money does she have to pay for 3 liters?
Solution:
Given,
Janci ordered 5liters of oil for= Rs 550
Cost of 1-liter oil=Rs 550/5=Rs110
Cost of 3-liter oil=3 × 110=Rs 330
Therefore, Janci has to pay Rs 330.
Ix. A car traveling at a speed of 100 kmph covers 320 km. How much time will it take to cover 220 km?
Solution:
Given,
A car traveling at a speed of 100 kmph covers= 320 km
First, we have to find the time required to cover 320 km.
Speed = Distance/Time
100 = 320/T
T = 3.2 hours
Applying the unitary method,
320 km = 3.2 hours
1 km = 3.2/320 hour=0.01
220 km = 0.01 x 220 = 2.2 hours
Therefore, it will take 2.2 hours to cover 220km.
X. Ajay finishes his work in 20 days while Bhaskar takes 30 days. How many days will the same work be done if they work together?
Solution:
Given,
Ajay finishes his work in =20 days
Bhaskar finishes his work in=30 days
Ajay’s 1 day work=1/20
Bhaskar’s 1 day work=1/30
Now, total work is done by A and B in 1 day = 1/20 + 1/30
Taking LCM(20, 30), we have,
1 day’s work of A and B = (3+2)/60=5/60=1/12
1 day’s work of (A + B) = 1/12
Thus, A and B can finish the work in 12 days if they work together.
XI. A train is moving at a uniform speed of 58 km per hour. How far will it go in 10 minutes?
Solution:
Given,
A train is moving at a uniform speed of =58 km per hour
We know that speed=distance/time
First, we have to convert 10 minutes to hours.
To convert minutes to hours we have to divide it by 60.
10/60=0.16
58km=distance/0.16
distance=58 x 0.16=9.28
Hence, the train will move 9.28 km in 10 minutes.