Page 95 - ICSE Math 7

Final quantity
Therefore, multiplying ratio =
Original quantity
5 b
In the above examples, and are the multiplying ratios.
4 a
Example 6: Find the multiplying ratio which changes 96 kg to 69 kg.
Final quantity 69 23
Solution: Multiplying ratio = = =
Original quantity 96 32
Example 7: The number of plants in a garden was 222 in the year 2011. In 2012, the number of plants
increased in the ratio 3 : 4. Then in 2013, the number of plants decreased in the ratio
2 : 1. Find the number of plants in the garden in 2013.
4
Solution: Number of plants in 2012 = × number of plants in 2011
3
4
= × 222 = 296
3
1
Number of plants in 2013 = × number of plants in 2012
2
1
= × 296 = 148
2

To Divide a Given Quantity in a Given Ratio

Dividing into two parts
Suppose A is to be divided in the ratio x : y, then
 x   y 
First part =  x +  × A and Second part =  x +  × A


y
y


Dividing into three parts
Suppose A is to be divided in the ratio x : y : z, then
 x   y   z 
First part =  x ++  × A, Second part =  x ++  × A and Third part =  x ++   × A


z
z
y
y



y
z
Example 8: A number is divided into two parts in the ratio 5 : 11. If the first part is 225, then find
the number.
Solution: Let the number be x.
 5 
First part =   511+ 

5 16
⇒ 225 = × x ⇒ x = 225 × = 720
16 5
Thus, the required number is 720.
Example 9: A man divides his property of ` 1,50,000 among his three children in the ratio 2 : 3 : 5.
Find the share of each child.
 2  2
Solution: Share of first child =  23 5++   × ` 1,50,000 = 10 × ` 1,50,000 = ` 30,000

 3  3
Share of second child =   × ` 1,50,000 = × ` 1,50,000 = ` 45,000
 23 5++  10
 5  5
Share of third child =   × ` 1,50,000 = × ` 1,50,000 = ` 75,000
 23 5++  10

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