Discussion
45% of first number is equal to the 60% of the second number. If average of both the numbers is 10 less than the first number, then find 80% of second number.
Answer: C
80% of the second number is 48.
Let the numbers be \(a\) and \(b\). From \(0.45a = 0.6b\), \(a = \frac{4}{3}b\). Their average is 10 less than \(a\).
\[ \begin{aligned} \frac{a + b}{2} &= a - 10 \\ b &= a - 20 = \frac{4}{3}b - 20 \\ b &= 60,\ a = 80 \end{aligned} \]
So 80% of 60 is 48. Check: 45% of 80 = 36 = 60% of 60, and the average 70 is 10 less than 80. 64 is 80% of the first number.
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