120 is divided into two parts in such a way that the seventh part of first and the fifth part of second are in the ratio 5 : 17. What will be the value of second part?

120 is divided into two parts in such a way that the seventh part of first and the fifth part of second are in the ratio 5 : 17. What will be the value of second part?

(A) 85 (B) 68

(C) 51 (D) 35

Let’s denote the two parts as \(x\) and \(120 – x\).

According to the given information:

\[\frac{1}{7}x : \frac{1}{5}(120 – x) = 5 : 17\]

Now, we can set up the equation and solve for \(x\):

\[\frac{x}{7} : \frac{1}{5}(120 – x) = 5 : 17\]

To simplify, multiply both sides by the common multiple of 7 and 5, which is 35:

\[5x : 7(120 – x) = 5 \times 5 : 17 \times 5\]

\[5x : 840 – 7x = 25 : 85\]

Now, cross-multiply:

\[85(5x) = 25(840 – 7x)\]

\[425x = 21000 – 175x\]

Combine like terms:

\[425x + 175x = 21000\]

\[600x = 21000\]

Divide by 600:

\[x = \frac{21000}{600}\]

\[x = 35\]

So, the first part (\(x\)) is 35, and the second part (\(120 – x\)) is \(120 – 35 = 85\).

Therefore, the value of the second part is 85. Hence, the correct answer is (A) 85.

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