Question
Download Solution PDFTwo 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
Last updated on Jun 2, 2025
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