Page 93 - ICSE Math 8

5. Rajan and Rohit had a total of 468 coins in the ratio 11 : 7. Rajan’s mother gave him 14 more coins and
Rohit’s mother took a few coins from Rohit. Now, the new ratio of coins is 15 : 8. How many coins does
Rohit have?
6. The ratio of the number of boys to the number of girls in a school with 840 students was 7 : 5. In the new
session, the number of boys increased by 20 and the ratio of boys to girls changed to 6 : 5. Calculate the
number of new girls.
7. A 72 L mixture contains milk and water in the ratio 7 : 5. How much more milk is to be added to the
mixture so that the new ratio of milk and water becomes 9 : 5?
8. If x : y = 7 : 9 and y : z = 11 : 14, find: (a) x : y : z (b) x : z
1 2 2 2
9. If A : B = 2 : 1 and B : C = 3 : 2 , find: (a) A : B : C (b) A : C
3 3 3 3
10. If 70X = 21Y = 14Z, find X : Y : Z.
 K K K 
 Hint: Let 70X = 21Y = 14Z = K , i.e., X = , Y = ,Z = 
 70 21 14 

Proportion
When two ratios are equal, they are said to be in proportion if the ratio of the first to the second quantity
is same as the ratio of the third to the fourth quantity. If p, q, r and s are in proportion, it is denoted by
p : q :: r : s and is read as ‘p is to q as r is to s’. The four quantities in a proportion are called its terms.
In proportion a : b :: c : d, a, b, c and d are the first, second, third and fourth terms respectively. The fourth
term is also called the fourth proportional to the terms a, b and c. Also, the first and the fourth terms are
called extremes and the second and the third terms are called means. For example, ratio between 16 and 40 =
16 2 30 2
16 : 40 = 40 = = 2 : 5 and ratio between 30 and 75 = 30 : 75 = 75 = = 2 : 5. Therefore, the four quantities
5
5
are in proportion, i.e., 16 : 40 :: 30 : 75.
Point to remember
The product of extremes is equal to the product of means, which is known as cross-product rule.

Example 6: Find the value of x if 12 : 6 :: x : 9.
Solution: 12 : 6 :: x : 9
12 × 9
⇒ 6x = 12 × 9 ⇒ x = 6 = 18 (Product of extremes = Product of means)

Example 7: Find the fourth proportional to 7, 12 and 21.
Solution: Let the fourth proportional be x.
So, 7 : 12 :: 21 : x
12 × 21
⇒ 7x = 12 × 21 ⇒ x = 7 = 36 (Product of extremes = Product of means)

Continued Proportion

Three quantities of the same kind are said to be in continued proportion if the ratio between the first and
the second quantity is equal to the ratio between the second and the third quantity. Thus, if a, b and c are in
a
b
2
continued proportion, then a : b = b : c, i.e., = ⇒ b = ac.
c
b
Points to remember
• The third quantity is called the third proportional to the first and second quantity.
• The second quantity is called the mean proportional between the first and the third quantity.

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