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.
