Question

two numbers are in the same ratio 6:11. on adding 2to the first and 7 to the second there ratio becomes 8:15 find the number

Answer 1

Answer:

1st number = 78

2nd number = 143

Step-by-step explanation:

Let the constant be x

Given, two numbers are in the ratio 6 : 11

So, let the two numbers be 6x and 11x

Adding, 2 to the first and 7 to the second = 6x + 2 and 11 + 7

After adding, the ratio of the numbers becomes = 8 : 15

____________________________

According to the question,

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

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

=> 90x + 30 = 88x + 56

=> 90x - 88x = 56 - 30

=> 2x = 26

=> x = $\dfrac{26}{2}$

=> x = 13

____________________________

1st number => 6x

=> 6 * 13

=> 78

2nd number => 11x

=> 11 * 13

=> 143

Answer 2

let two numbers be 6x , 11x

On adding 2 to first

So it becomes 6x +2

and 7 to second

it becomes 11x +7

ratio becomes 8:15

So (6x+2)/( 11x+7)= 8/15

Apply componendo and dividendo

6x+2+ 11x +7)/ 6x+2 -11x -7= 8+15)/8-15

= 17x +9)/ -5x -5= 23/-7

17x+9)/5x +5= 23/7

17x+9)/ x+1 = 115/7

119x + 63 = 115x +115

4x = 52
x=13

So original no's are 6x,11x

6× 13 = 78

11× 13= 143

So 78 and 143 are original no's.


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