Question

94 is divided into two parts such that fifth part of first and eighth part of second are in the ratio 3:4 then first part is
A) 36
B) 28
C) 30
D) 32

Answer 1

Hint:
We will use all the information given in the question. First divide the number in two parts as x and 94-x. Then take the fifth part of first and eighth part of second. Now their ratio is 3:4. Then equate and find the value of x that is the first part.

Complete step by step solution:
Given that 94 is divided into two parts.
Let x be the first part and then 94-x will be the second part.
Now we have to take the ratio of the fifth part of first and eighth part of second.
So,
\[ \Rightarrow \dfrac{{\dfrac{x}{5}}}{{\dfrac{{94 - x}}{8}}}\]
But this is in the ratio 3:4.
\[ \Rightarrow \dfrac{{\dfrac{x}{5}}}{{\dfrac{{94 - x}}{8}}} = \dfrac{3}{4}\]
Rearranging the terms,
\[ \Rightarrow \dfrac{{8x}}{{5\left( {94 - x} \right)}} = \dfrac{3}{4}\]
On cross multiplying,
\[
   \Rightarrow 4 \times 8x = 15\left( {94 - x} \right) \\
   \Rightarrow 32x = 15 \times 94 - 15x \\
\]
Taking x terms on one side,
\[
   \Rightarrow 32x + 15x = 15 \times 94 \\
   \Rightarrow 47x = 15 \times 94 \\
   \Rightarrow x = \dfrac{{15 \times 94}}{{47}} \\
   \Rightarrow x = 15 \times 2 \\
   \Rightarrow x = 30 \\
\]

Thus the first part is x and its value is 30.
So the correct option is C.

Note:
Please note that 94 is not divided into two equal parts. And we are asked to find the first part of the number and not the second. You can take the second part as x and first as 94-x but remember it when you put it in front of the ratio. Then ratio will be,
\[ \Rightarrow \dfrac{{\dfrac{{94 - x}}{5}}}{{\dfrac{x}{8}}} = \dfrac{4}{3}\]