HCF and LCM of two numbers P and Q are 16 and 560 respectively and when 8 is added to P and 20 is added to Q, then HCF and LCM become 20 and 600 respectively, then what is the ratio of the value of P to Q? Assume both P and Q are more than 50.

HCF and LCM of two numbers P and Q are 16 and 560 respectively and when 8 is added to P and 20 is added to Q, then HCF and LCM become 20 and 600 respectively, then what is the ratio of the value of P to Q? Assume both P and Q are more than 50. Correct Answer 7 : 5

Given:

HCF (P, Q) = 16

LCM (P, Q) = 560

Formula Used:

First number × Second number = HCF × LCM

Calculation:

P × Q = 16 × 560

⇒ PQ = 8960      ----(i)

(P + 8) × (Q + 20) = 20 × 600

⇒ PQ + 20P + 8Q + 160 = 12000      ----(ii)

From (i) and (ii):

8960 + 20P + 8Q + 160 = 12000

⇒ 20P + 8Q = 2880 ……. (iii)

From (i) and (iii) we get 

Q = 80 and 280 

P = 32 and Q = 280

⇒ P = 112 and Q = 80

∴ Required ratio = P : Q

= 112: 80

= 7: 5