Question 55

The ratio between two given numbers is 9 : 7. If each number is increased by 6, then the ratio becomes 21 : 17. What is the difference between the two given numbers?

Solution

The ratio between two given numbers is 9 : 7.

Let's assume the two given numbers are 9y and 7y respectively.

If each number is increased by 6, then the ratio becomes 21 : 17.

$$\frac{9y+6}{7y+6}\ =\ \frac{21}{17}$$

$$\frac{3y+2}{7y+6}\ =\ \frac{7}{17}$$

51y+34 = 49y+42

51y-49y = 42-34

2y = 8

Difference between the two given numbers = (9y-7y)

= 2y

= 8

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