Question

What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?

What number must be subtracted from each of number 7, 17, 47 so that the remainder may be in continued proportion?

Answer 1

Let the number subtracted be x.

∴ (7 – x) : (17 – x) :: (17 – x)(47 – x)

⇒ `(7 - x)/(17 - x) = (17 - x)/(47 - x)`

⇒ (7 – x) (47 – x) = (17 – x) (17 – x)

Left side:

7 × 47 − 7x − 47x + x² = 329 − 54x + x²

Right side:

(17−x)² = 289 − 34x + x²

⇒ 329 − 54x + x² = 289 − 34x + x²

⇒ 329 − 54x = 289 − 34x

⇒ 329 – 289 = 54x − 34x

⇒ 40 = 20x

⇒ x = `20/40`

⇒ x = 2

Thus, the required number which should be subtracted is 2.