Page 234 - Start Up Mathematics_6

6. Find x if 25, 35, x are in continued proportion.

7. Anant covers a distance of 225 km in 5 hours in his car. How much distance will he be able
to cover in 7 hours? Find the answer using proportions.
8. The ratio of income and expenditure of a family is 10 : 9. Find the savings if the income of
the family is ` 60,000.
9. The ratio of trousers and shirts in the wardrobe of Mr Hussain is 3 : 5. If the number of shirts
is 20, find the number of trousers in the wardrobe.

Unitary Method
The method of finding the value of one unit and then the value of the required number of units is
known as the unitary method. Let’s consider the following situation.

If the cost of 5 kg apples is ` 200, what is the cost of 3 kg apples? Here, we first need to find the
cost of 1 kg apple and then the cost of 3 kg apples.
Cost of 5 kg apples = ` 200

Cost of 1 kg apples = ` 200 ÷ 5 = ` 40
Therefore, the cost of 3 kg apples = ` 40 × 3 = ` 120. This method is called unitary method.
Example 17: If the cost of 6 m cloth is ` 528, find the cost of 9 m cloth.

Solution: Cost of 6 m cloth = ` 528
Cost of 1 m cloth = ` 528 ÷ 6 = ` 88

Therefore, cost of 9 m cloth = ` 88 × 9 = ` 792
Example 18: If it has rained 276 mm in the last 3 days, how many cm of rain will fall in one full
week (7 days)? Assume that the rain continues to fall at the same rate. (NCERT)

Solution: Rainfall in 3 days = 276 mm
Rainfall in 1 day = 276 ÷ 3 = 92 mm

Therefore, rainfall in 7 days = 92 mm × 7 = 644 mm = 64.4 cm
Example 19: Cost of 10 kg of rice is ` 325.
(a) What will be the cost of 8 kg of rice?

(b) What quantity of rice can be purchased with ` 130?
Solution: Cost of 10 kg rice = ` 325

Cost of 1 kg rice = ` 325 ÷ 10 = ` 32.5
(a) Cost of 8 kg rice = ` 32.5 × 8 = ` 260

(b) Quantity of rice that can be purchased with ` 130 = ` 130 ÷ ` 32.5 = 4 kg
Example 20: Devika pays ` 9,000 as rent for 5 months. How much will she have to pay for a
whole year, if the rent per month remains same?

Solution: Rent for 5 months = ` 9,000
Rent for 1 month = ` 9,000 ÷ 5 = ` 1,800
Therefore, rent for 1 year (12 months) = ` 1,800 × 12 = ` 21,600

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