Find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second numbers added to the difference of the third and the second numbers is 42.
Explanation:
Let the numbers be p, q and r.
Given that p, q and r are in the ratio 3 : 2 : 4.
p : q : r = 3 : 2 : 4
Let p = 3x, q = 2x and r = 4x
Given (p + q) + (r – q) = 42
⇒ p + q + r – q = 42 ⇒ p + r = 42
⇒ 3x + 4x = 42
⇒ 7x = 42
⇒ x = 6
p, q, r are 3x, 2x, 4x.
∴ p, q, r are 18, 12, 24
Hence, option (d).
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