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1. The difference between two numbers is 16. If one-third of the smaller number is greater than one-seventh of the larger number by 4, then the two numbers are :

A. 9 and 25

B. 12 and 28

C. 33 and 49

D. 56 and 72

Solution:

Let the numbers be x and (x + 16)
Then,

\begin{aligned} \Leftrightarrow \frac{x}{3} - \frac{(x + 16)}{7} = 4 \\ \Leftrightarrow 7 x - 3 (x + 16) = 84 \\ \Leftrightarrow 4 x = 84 + 48 \\ \Leftrightarrow 4 x = 132 \\ \Leftrightarrow x = 33 \end{aligned}

Hence, the numbers are 33 and 49

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