If the sum of two natural numbers is multiplied by each number separately, the products so obtained are 2772 and 1584. What is the difference between the numbers?
Explanation:
Suppose numbers are x and y, we have
x(x + y) = 2772 (i) y(x + y) = 1584 (ii)
Adding (i) and (ii), we get (x + y)2 = 4356 ∴ x + y = 66 (iii)
Subtracting (ii) from (i), we get x2 – y2 = 1188 ⇒ (x + y) × (x – y) = 1188
⇒ 66 × (x – y) = 1188 using (iii) ∴ x – y = 18
Hence, option (a).
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