Two numbers P and Q are such that the sum of 10% of P and 15% of Q is three-fourths of the sum of 20% of P and 18% of Q. Find the ratio of P : Q.

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A

10 : 3

B

3 : 7

C

5 : 12

D

3 : 10

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Question: Two numbers P and Q are such that the sum of 10% of P and 15% of Q is three-fourths of the sum of 20% of P and 18% of Q. Find the ratio of P : Q.


Solution:

10% of P + 15% of Q = 3/4 × (20% of P + 18% of Q)

⇒ 10P/100 + 15Q/100 = 3/4 × (20P/100 + 18Q/100)

⇒ P/10 + 3Q/20 = 3/4 × (P/5 + 9Q/50)

⇒ 2P/20 + 3Q/20 = 3/4 × (10P + 9Q)/50

⇒ (2P + 3Q)/20 = (30P + 27Q)/200

⇒ 10(2P + 3Q) = 30P + 27Q

⇒ 20P + 30Q = 30P + 27Q

⇒ 30Q - 27Q = 30P - 20P

⇒ 3Q = 10P

⇒ P/Q = 3/10

∴ P : Q = 3 : 10

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Updated: 5 days ago

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