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What two parts are generated when we divide 184 into two parts such that one-third of one part may exceed one-seventh of the other part by 8?

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72, 34

72, 112

112, 113

14, 15

answer is B.

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Detailed Solution

Given, we divide 184 into two parts such that one-third of one part may exceed one-seventh of the other part by 8.
Let the two parts be x and y.
According to the question,

\frac{x}{3} = \frac{y}{7} + 8

.
Also,

x + y = 184

y = 184 - x

substitute above equation in

\frac{x}{3} = \frac{y}{7} + 8

\frac{x}{3} = \frac{184 - x}{7} + 8

LCM between any number with one is the number itself.
So, the LCM between 1 and 7 is 7.

\frac{x}{3} = \frac{184 - x + 56}{7}

7 x = 3 (240 - x)

7 x = 720 - 3 x

10x = 720
x = 72.
The other part is

184 - x = 112

.
Therefore the parts are 72 and 112.
Hence option 2 is correct.

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