Question

If 45 is subtracted from twice the greater of two numbers, it results in the other number. If 21 is subtracted from twice the smaller number, it results in the greater number. Find the numbers

Answer 1

Let the greater number be x and the smaller number be y.
Then, we have:
25x – 45 = y or 2x – y = 45                         ……….(i)
2y - 21 = x or –x +2y = 21                       ………(ii)
On multiplying (i) by 2, we get:
4x - 2y = 90                                                ………..(iii)
On adding (ii) and (iii), we get
3x = (90 + 21) = 111
⇒ x = 37
On substituting x = 37 in (i), we get
2 × 37 - y = 45
⇒ 74 - y = 45
⇒ y = (74 - 45) = 29
Hence, the greater number is 37 and the smaller number is 29.