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## Direct Variation using Method of Proportion Worksheet with Answers

I. The cost of 7 kg of sugar is Rs  210. What will the cost of 13 kg of sugar be?

Solution:

Given,
The cost of 7 kg of sugar is = Rs 210
Let the cost of 13 kg of sugar be x.
Since they vary directly,
7/210=13/x
7x=210 × 13
7x=2730
x=2730/7=390
Hence, the cost of 13 kg of sugar is Rs 390.

II. If the weight of 4 fruits is 500 g, find how many such fruits will weigh 5.5 kg?

Solution:

Given,
The weight of 4 fruits is= 500 g
The weight of 1 fruit=500/4=125
we know that 1 kg=1000 gm.
5.5 kg=5500 gm
No. of fruits will weigh 5.5 kg=5500/125=44
Hence, 44 fruits will weigh 5.5 kg.

III. Rakesh gets Rs 3500 for 7 days of work. How many days should he work to get Rs 8000?

Solution:

Given,
Rakesh gets money for 7 days of work=Rs 3500
Two quantities vary directly, (money and working days)
i.e. More money more working days.
Let the number of working days to get the money of Rs 8000 be x.
7/3500=x/8000
56000=3500x
x=56000/3500
x=16
Therefore, Rakesh has to work 16 days to get Rs 8000.

IV. The cost of  8 notebooks is Rs192, what do 30 notebooks cost?

Solution:

Given,
The cost of  8 notebooks is=Rs 192
Let the cost of 30 notebooks be x.
since they vary directly,
8/192=30/x
8x=30 × 192
8x=5760
x=5760/8
=720
Hence, the cost of 30 notebooks is Rs 720.

V. A man walks 10,000 steps every day to cover a 1 km distance. If he walks 14,000 steps how much distance will be covered?

Solution:

Given,
A man takes 10000 steps every day to cover a distance=1 km
Let the distance covered for 14000 steps be x.
since they vary directly,
10000/1=14000/x
10000x=14000
x=14000/10000
=1.4
Hence, the man covers 1.4 km if he walks 14,000 steps.

VI. At a birthday party, Ravi buys 8 gallons of juice for 70 members. how many gallons do they need for 180 members?

Solution:

Given,
Ravi buys juice for 70 members=8 gallons
Let the 180 members need gallons of juice be x.
since they are in direct variation,
70/8=180/x
70x=8 × 180
70x=1440
x=1440/70=20.57
Therefore, Ravi needs 20.57 gallons of juice for 180 members.

VII. A bus travels 120 km on 5 liters of petrol. How far would it travel in 4 liters of petrol?

Solution:

Given,
A bus travels120 km with no. of liters of petrol=5 liters
Let the bus travels the no. of km with 4 liters of petrol be x.
120/5=x/4
480=5x
x=480/5=96
Therefore, the bus travels 96 km with 4 liters of petrol.

VIII. 9 workers can dig 7 m long trench in one day. How many workers would dig 25 m long trench of the same type in 1 day?

solution:

Given,
No. of workers can dig 7 m long trench in one day=9
Let the no. of workers dig 25 m long trench in one day=x
Since they are in direct proportion,
7/9=25/x
7x=225
x=225/7=32
Therefore, 32 workers were required to dig a trench in one day.

IX. If two pens cost Rs 50, how many pens can you buy for Rs 250?

Solution:

Given,
Two pens cost= Rs 50
Let the number of pens can buy for Rs 250 is x.
2/50=x/250
2 × 250=50x
500=50x
x=500/50=10
Therefore, 10 pens can be bought for Rs 250.

X. 3 bags of wheat weigh 150 kg. How many such bags will weigh 900 kg?

Solution:

Given,
Weight of 3 bags of wheat=150 kg
Let the number of bags weighing 900 kg be x.
since it is direct proportion,
3/150=x/900
2700=150x
x=2700/150
=18
Therefore, 18 bags of wheat will weigh 900kg.