Question

two numbers are in ratio 6:11 .ON ADDING 2 TO THE FIRST AND 7 TO the second .their ratio become 8:15.find the number

Answer 1

let be the number s are x and y

first condition

x:y = 6:11

x/y = 6/11

11x = 6y

x = 6y/11......................,...............(1)

(x+2)/(y+7) = 8:15

15(x+2) = 8(y+7)

15x +30 = 8y + 56

15x - 8y = 56-30

15 x - 8y= 26........,...............(2)



putting the value of x in equation (2) from (1)

15×6y/11 - 8y = 26

90y /11 -8y = 26


multiple by 11 in both sides


90y -88y = 286


2y = 286


y = 143



putting the value of y in equation (1)



x = 6×143/11

x = 78


x=78
y= 143


hope it helpful for you

Answer 2

Let the two numbers be 6x and 11x

On adding 2 to the first number = ( 6x + 2 )

On adding 7 to the second number = ( 11x + 7 )

Their ration becomes 8 : 15

Therefore, the numbers becomes 15(6x + 2) and 8(11x + 7)


ATQ,

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

90x + 30 = 88x + 56

90x - 88x = 56 - 30

2x = 26

x = $\frac{26}{2}$

x = 13



1st number = 6x = 6 × x = 6 × 13 = 78

2nd number = 11x = 11 × x = 11 × 13 = 143