Question
Download Solution PDFTwo numbers are in the ratio of 3 : 5. If 6 is subtracted from each, the new numbers are in the ratio 9 : 17. The smaller number is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
m : n = 3 : 5
(m - 6) : (n - 6) = 9 : 17
Calculation:
⇒ 5m = 3n
⇒ 5m - 3n = 0 →(1)
⇒ 17(m - 6) = 9(n - 6)
⇒ 17m - 102 = 9n - 54
⇒ 17m - 9n = 48 →(2)
Subtracting the [equation (1) multiplied by 3] from equation (2),
⇒ 17m - 9n - 15m + 9n = 48 - 0
⇒ 2m = 48
⇒ m = 24
From Eqn (2), we have
⇒ n = (5 × 24)/3 = 40
∴ The smaller number is 24.
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