Question
Download Solution PDFThe ratio between a two digit number and the number obtained by reversing its digits is 4 ∶ 7. What is the sum of all such possible pairs of numbers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The ratio between a two digit number and the number obtained by reversing its digits is 4 : 7.
Calculation:
Let the two-digit number be 10a + b and the number obtained by reversing its digit be 10b + a
⇒ (10a + b)/(10b + a) = 4/7
⇒ 70a + 7b = 40b + 4a
⇒ 66a = 33b
⇒ a/b = 1/2
possible two digit pairs are (12, 21), (24, 42), (36, 63), (48, 84)
sum of all such possible pairs = (12 + 21 + 24 + 42 + 36 + 63 + 48 + 84) = 330
∴ the correct answer is 330.
Last updated on Apr 9, 2025
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