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Do Check: Worksheet on Direct Variation using Unitary Method

## 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.