Question

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

Answer 1

Let the two numbers be x and y.

By the given first condition

x : y = 5 : 6

6x = 5y ...(Product of the extreme is equal to the product of the means)

6x – 5y = 0 → (1)

Again by the given second condition

x – 8 : y – 8 = 4 : 5

5(x – 8) = 4(y – 8)

5x – 40 = 4y – 32

5x – 4y = – 32 + 40

5x – 4y = 8 → (2)

(1) × 4 ⇒ 24x – 20y = 0 → (3)

(2) × 5 ⇒ 25x – 20y = 40 → (4)

(3) – (4) ⇒ – x + 0 = – 40

∴ x = 40

Substitute the value of x = 40 in (1)

6(40) – 5y = 0

240 – 5y = 0 ⇒ – 5y = – 240

5y = 240

y = `240/5`

= 48

The two numbers are 40 and 48 ...[∴ The ratio of the number = 40 : 48 are 5 : 6]