Question

If Rs.60 is divided into two parts in the ratio 2:3, then the difference between those parts is?
A) \[Rs.10\]
B) \[Rs.12\]
C) \[Rs.5\]
D) None of the above

Answer 1

Hint: To find the required difference between two parts first of all we have to find the required parts by framing an equation as per the information given in the question. Then after solving the given equation in order to get the required difference.

Complete step by step answer:
Let the ratio be \[2x\] and \[3x\].
According to the question,
\[
   \Rightarrow 2x + 3x = 60 \\
   \Rightarrow 5x = 60 \\
   \Rightarrow x = 12. \\
\]
Therefore the required parts are:
\[ 3x = \left( {3 \times 12} \right) \\
   \Rightarrow 3x = 36 \\
\]
and
\[ 2x = \left( {2 \times 12} \right) \\
   \Rightarrow 2x = 24 \\
\]
Hence, the required difference between two parts\[\left( {3x - 2x} \right) = 36 - 24 = 12\]
\[x = 12\].

Option (B) is the correct answer.

Note:
If we substitute an amount in any ratios, then the sum of the ratios will be equal to the sum of the amount.
Another approach to solve this problem would be
First part = \[\left( {\dfrac{2}{5}} \right) \times 60\]
\[ \Rightarrow \] First part = \[24\]…………….. (i)
Second part = \[\left( {\dfrac{3}{5}} \right) \times 60\]
\[ \Rightarrow \] Second part =\[36\]……………… (ii)
Subtracting equation (i) from (ii), we get:
Hence, the required difference \[\left( {36 - 24} \right) = 12.\]

In order to tackle these kinds of problems one should go through with any one of the methods (Illustrated or direct method) to solve this question and have to practice more word problems from the topic of ratio and proportion.