Question

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

Answer 1

Answer:

Let the two numbers be 6x and 11x as their ratio is 6:11

Given 2 is added to first and 7 is added to second

Hence the numbers become, (6x + 2) and (11x + 7)

Given (6x + 2) : (11x + 7) = 8:15

Hence 15(6x + 2) = 8(11x + 7)

90x + 30 = 88x + 56

2x = 26

Therefore, x = 13

Hence the numbers are 6x = 6(13) = 78

11x = 11(13) = 143

Answer 2

Given :

• Two numbers are in the ratio 6:11.
• If 2 is added to the first and 7 to the second then the ratio becomes 8:15.

To Find :

• Numbers.

Solution :

$\longmapsto\tt{Let\:first\:no\:be=6x}$

$\longmapsto\tt{Let\:second\:no.\:be=11x}$

Now ,

On adding 2 to the first no. and 7 to the second the ratio becomes 8:15. So ,

$\longmapsto\tt{First\:No.=6x+2}$

$\longmapsto\tt{Second\:No.=11x+7}$

A.T.Q :

$\longmapsto\tt{\dfrac{6x+2}{11x+7}=\dfrac{8}{15}}$

$\longmapsto\tt{15(6x+2)=8(11x+7)}$

$\longmapsto\tt{90x+30=88x+56}$

$\longmapsto\tt{90x-88x=56-30}$

$\longmapsto\tt{2x=26}$

$\longmapsto\tt{x=\cancel\dfrac{26}{2}}$

$\longmapsto\tt\bold{x=13}$

Value of x is 13...

Therefore :

$\longmapsto\tt{First\:No.=6(13)}$

$\longmapsto\tt\bold{78}$

$\longmapsto\tt{Second\:No.=11(13)}$

$\longmapsto\tt\bold{143}$