In this page ratio and proportion solution12 we are going to see solution of each question from the worksheet ratio and proportion.

(22) What number must be added each term of the ratio 5 : 7 so that it becomes 10 : 11

**Solution:**

Let “x” be the required number to be added

This term must be added to each term of ratio, then (5 + x) : (7 + x)

If x is added to both terms it will be equal to the ratio 10 : 11

So, (5 + x)/(7 + x) = 10 : 11

(5 + x)/(7 + x) = 10/11

11 (5 + x) = 10 (7 + x)

55 + 11 x = 70 + 10 x

11 x – 10 x = 70 – 55

x = 15

Therefore the required number to be added is 15.

(23) What number must be subtracted from each term of the ratio 23 : 44 so that the ratio becomes 6 : 13

**Solution:**

Let “x” be the required number to be subtracted

This term must be subtracted from each term of ratio, then (23 - x) : (44 - x)

If x is subtracted from to both then it will be equal to the ratio 6 : 13

So, (23 - x)/(44 - x) = 6 : 13

(23 - x)/(44 - x) = 6/13

13 (23 - x) = 6 (44 - x)

299 - 13 x = 264 - 6 x

-13 x + 6 x = 264 – 299

- 7 x = -35

x = (-35)/(-7)

x = 5

Therefore the required number to be subtracted is 5.

(24) Find two numbers in the ratio 5 : 7 deferring by 12.

**Solution:**

Let "x" and "x -12" are the required two numbers

x : (x-12) = 5 : 7

x/(x- 12) = 5/7

7 x = 5 (x - 12)

7 x = 5 x - 60

7 x - 5x = - 60

2 x = -30

x = -30/2

x = -15

Therefore the first required number is -15 and the second number is -15 - 12 = - 27

ratio and proportion solution12 ratio and proportion solution12

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