Question

(b) two numbers are in the ratio 5:6. if 8 is subtracted from each of the numbers, the ratio becomes 4:5. find the number

Answer 1

the numbers are 40 and 48

Explanation:

two numbers in the ratio 5 : 6 = 5x : 6x ( x is a multiplier )

subtracting 8 from each number gives ratio 4 : 5 , that is

5x - 8 : 6x - 8 = 4 : 5

expressing the ratios in fractional form , that is

`(5x-8)/(6x-8)` =
`(4)/(5)` ( cross- multiply )

5(5x - 8) = 4(6x - 8) ← distribute parenthesis on both sides

25x - 40 = 24x - 32 ( subtract 24x from both sides )

x - 40 = - 32 ( add 40 to both sides )

x = 8

the required numbers are

5x = 5 × 8 = 40

6x = 6 × 8 = 48