Question

1. Two numbers are in the ratio of 5 : 7. If 18 is added to each of the
number, the ratio becomes 7: 8. Find the numbers.
[Ans. 10 and 14]
Two numbers are in the ratio of 4: 5. If 10 be added to each number,​

Answer 1

Step-by-step explanation:

let two numbers 5X and 7X

5X+18 / 7X+ 18 = 7/8

9X = 18

X= 2

so numbers 10,14

Answer 2

The numbers are 10 and 14.

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Let's solve the given problem:

The ratio of the two numbers is 5 : 7

So, let's say,

"5x" and "7x" represents the two numbers.

On adding 18 to each of the numbers, the new ratio becomes 7 : 8. So, we can form an equation as,

$\frac{5x\:+ \:18}{7x \:+\: 18} = \frac{7}{8}$

$\implies 8 (5x + 18 ) = 7 (7x + 18)$

$\implies 40x + 144 = 49x + 126$

$\implies 49x - 40x = 144 - 126$

$\implies 9x = 18$

$\implies x = 2$

Therefore,

$5x = 5\times 2 = \bold{10}$

and

$7x = 7\times 2 = \bold{14}$

Thus, the numbers are 10 and 14.

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