If the sum of LCM and HCF of two numbers is . . .

Question : If the sum of LCM and HCF of two numbers is 50 and their LCM is 20 more than their HCF. Then the product of the two numbers will be

a) 525

b) 425

c) 625

d) 325

Doubt by Gauri

Solution :

LCM + HCF = 50 — (1)

LCM = 20 + HCF — (2)

20+HCF + HCF = 50
2HCF = 50-20

2HCF = 30
HCF = 30/2
HCF = 15

LCM = 20 + 15 [Using (2)]

LCM = 35

We know,
a×b = LCM×HCF
a×b = 35×15
a×b = 525

Hence, a) would be the correct option.

Class 10