The sum of the two position number P and Q is 2.5 time their

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The sum of the two position number P and Q is 2.5 time their difference .If the product of the number 84 then the what is the sum of those two number?

1. 26
2. 24
3. 22
4. 20

Correct Option: D

Let the number be P and Q
According to the question
(P + Q) = 2.5 (P - Q)
⇒ P + Q = 2.5P - 25Q
⇒ 3.5Q = 1.5P
⇒ P / Q = 7/3 .....(i)
Now PQ = 84
⇒ Q² = (84 x 3) / 7
⇒ Q² = 36
∴ Q = 6
&ther4; P = (7/3) x 6 = 14

Sum of the number = P + Q = 14 + 6 = 20