Question

1. Two numbers are in the ratio 6: 11. On adding 2 to the first and 7 to the second, their ratio becomes
8:15. Find the numbers.​

Answer 1

Hope this helps...........

Answer 2

Step-by-step explanation:

Given:-

• Two numbers are in the ratio 6 : 11

• On adding 2 to the first number and 7 to the second number the ratio becomes 8 : 15.

To Find:-

• The two numbers.

Solution:-

Case 1:-

As, the ratio between the numbers are 6 : 11

Let the first number be 6x and

Second number be 11x

Case 2:-

If 2 is added to first number

The first number becomes = 6x + 2

If 7 is added to second number

The second becomes = 11x + 7

Given, The ratio becomes 8 : 15

$\sf \implies \dfrac{6x + 2}{11x + 7} = \dfrac{8}{15}$

By cross multiplication:-

$\sf \implies 15(6x + 2) = 8(11x + 7)$

$\sf \implies 90x + 30 = 88x + 56$

$\sf \implies 90x - 88x = 56 - 30$

$\sf \implies 2x = 26$

$\sf \implies x = \dfrac{26}{2}$

$\sf \implies x = 13$

The first number = 6x = 6 × 13 = 78

The second number = 11x = 11 × 13 = 143

$\large\underline{\boxed{\sf \therefore The \: two \: numbers \: are \: 78 \: and 143}}$