Question

Two numbers are in the ratio 4 : 7. If thrice the larger be added to twice the smaller, the sum is 59. Find the numbers.

Answer 1

Given,

Two numbers are in the ratio 4 : 7.

`y/x = 4/7`

`=> y = (4x)/7`   ...(1)

If thrice the larger be added to twice the smaller, the sum is 59.

3x + 2y = 59

`3x + 2 xx (4x)/7 = 59`

`3x + (8x)/7 = 59`

`=> (29x)/7 = 59`

`=> x = (59xx7)/29`

`x = 14 7/29`

`y = 4/7 xx 14 7/29`

`4/7 xx 413/29`

`= (4 xx 59)/29`

`= 8 4/29`

Hence, numbers are `= 8 4/29` and `14 7/29`