Two numbers X and Y are in ratio as 8 : 13. The LCM of these two numbers is 832. How much the value of Y is more than X?

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  1. 50
  2. 30
  3. 40
  4. 45

Answer (Detailed Solution Below)

Option 3 : 40
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Detailed Solution

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Given:

X : Y = 8 : 13

LCM = 832

Formula used:

If X = 8k and Y = 13k, then LCM = (X × Y) ÷ HCF

Also, when two numbers are in ratio a : b and LCM is given, use:

LCM = (Product of numbers) ÷ HCF

Calculation:

Let X = 8k, Y = 13k

⇒ LCM = (8k × 13k) ÷ HCF of (8k, 13k)

HCF of 8k and 13k = k (since 8 and 13 are co-prime)

⇒ LCM = (104k²) ÷ k = 104k

Given: LCM = 832

⇒ 104k = 832

⇒ k = 832 ÷ 104 = 8

⇒ X = 8k = 8 × 8 = 64

⇒ Y = 13k = 13 × 8 = 104

⇒ Y − X = 104 − 64 = 40

∴ The value of Y is 40 more than X.

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