Sum of two numbers is 384. H.C.F. of the numbers is 48.

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Sum of two numbers is 384. H.C.F. of the numbers is 48. The difference of the numbers is

1. 100
2. 192
3. 288
4. 336

Correct Option: C

Let the numbers be 48p and 48q , where p and q are co-primes.
∴ 48p + 48q = 384
⇒ 48 (p + q) = 384

⇒ p + q =	384	= 8 ........... (i)
	48

Possible and acceptable pairs of p and q satisfying this condition are : (1 , 7) and (3 , 5).
∴ Numbers are : 48 × 1 = 48 and 48 × 7 = 336
and 48 × 3 = 144 and 48 × 5 = 240
∴ Required difference = 336 – 48 = 288