Question

Two numbers are in the ratio 5 : 6. If 8 is subtracted from the numbers, the ratio becomes 4 : 5. Find the numbers.

Answer 1

Let the two numbers be x and y.

Then by first condition,

Ratio of these two numbers = 5 : 6

x : y = 5 : 6

⇒ `x/y = 5/6`

⇒ y = `(6x)/5`  .....(i)

And by second condition,

If 8 is subtracted from each of the numbers,

Then ratio becomes 4 : 5

⇒ `(x - 8)/(y - 8) = 4/5`

⇒ 5x – 40 = 4y – 32

⇒ 5x – 4y = 8   ......(ii)

Now, put the value of y from equation (i) in equation (ii), we get

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

⇒ 25x – 24x = 40

⇒ x = 40

Put the value of x in equation (i), we get

y = `6/5 xx 40`

= 6 × 8

= 48

Hence, the required numbers are 40 and 48.