Page 94 - ICSE Math 8

Example 8: Determine the third proportional to 3 and 27.

Solution: Let the third proportional be x.
∴ 3, 27 and x are in continued proportion.
27 × 27
⇒ 3 : 27 = 27 : x ⇒ 3x = 27 × 27 ⇒ x = 3 = 243

Example 9: Find the mean proportional between 6 and 54.
Solution: Let the mean proportional be x.
∴ 6, x and 54 are in continued proportion.

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⇒ 6 : x = x : 54 ⇒ x = 6 × 54 ⇒ x = 6 54× = 18
EXERCISE 8.2

1. Find the value of x for the following proportions.
(a) 4 : 12 :: 18 : x (b) x : 21 :: 15 : 63 (c) 6.25 : x :: 5 : 4 (d) 0.14 : 3.5 :: x : 7.5

2. Find the fourth proportional to the following.
3 4 7
(a) 7, 11, 28 (b) 72, 12, 18 (c) 1 , 1 ,
4
5 12
3. Find the third proportional to the following.
1 2
(a) 3 and 15 (b) 0.15 and 1.8 (c) 4 and 5
4. Find the mean proportional between the following.
(a) 7 and 343 (b) 1.6 and 14.4 (c) 24 and 37.5
5. Find the following.

(a) Mean proportional between 2.6 and 5.3 correct to two decimal places.
(b) Third proportional to 7.2 and 9.6 correct to one decimal place.
(c) Fourth proportional to 8, 10 and 12 correct to two decimal places.

Direct Proportion

When two quantities are related in such a way that an increase or decrease in Quantity 1 Quantity 2
the first quantity causes an increase or decrease in the second quantity, then the p r
two quantities are said to be in direct proportion. For direct proportion, write q s
the quantities in tabular form. Cross-multiply the ratios to get ps = qr.
Example 10: If the cost of 8 apples is ` 28, what is the cost of 15 apples?
Solution: The cost and number of apples are in direct proportion as an increase in the number of apples
will cause an increase in the cost of apples.
Let the cost of 15 apples be ` x. Apples Cost (in `)
8 28
∴ = ⇒ 8x = 15 × 28 8 28
15 x
15 × 28 15 x
⇒ x = 8 = 52.5

∴ Cost of 15 apples is ` 52.50.
Example 11: If 26 toffees can be bought for ` 39, how many toffees can be bought for ` 67.50?
Solution: Number of toffees and cost are in direct proportion.

Let x be the number of toffees that can be bought for ` 67.50.

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