Question

If A’s salary is 30% more than that of B, then how much percent is B’s salary less than that of A’s?
A. 30 %
B. 25 %
C. $$23\dfrac{1}{13} \%$$
D. $$33\dfrac{1}{13} \%$$

Answer 1

Hint: In this question it is given that A’s salary is 30% more than that of B. Then we have to find how much percent is B’s salary less than that of A’s. So here A’s salary is dependent upon B, so we have to start our solution by considering the salary of B. After that when we will get A’s salary then we can easily find that how much percent is B’s salary less than that of A’s.

Complete step-by-step solution:
Let us consider the salary of B is x.
Therefore here it is given A’s salary is 30% more than that of B.
So we can write,
A’s salary =( B’s salary +30% of B’s salary)
                 =$$\left( x+\dfrac{30}{100} \times x\right) $$
                 =$$\left( x+\dfrac{3x}{10} \right) $$
                 =$$\dfrac{10x+3x}{10}$$
                 =$$\dfrac{13x}{10}$$
Therefore we get the salary of B and as well as the salary of A.
Now we have to find the percentage of the difference of their salary w.r.t A’s salary,
Difference of their salary =(A’s salary - B’s Salary)
                                        =$$\dfrac{13x}{10} -x$$
                                        =$$\dfrac{13x-10x}{10}$$
                                        =$$\dfrac{3x}{10}$$
Therefore, the percentage of difference of their salary w.r.t A is
$$=\dfrac{\text{Difference} }{\text{A’s salary} } \times 100\%$$
$$=\dfrac{\left( \dfrac{3x}{10} \right) }{\left( \dfrac{13x}{10} \right) } \times 100\%$$
$$=\dfrac{3x}{10} \times \dfrac{10}{13x} \times 100\%$$ [$$\because \dfrac{\left( \dfrac{a}{b} \right) }{\left( \dfrac{c}{d} \right) } =\dfrac{a}{b} \times \dfrac{d}{c}$$]
$$=\dfrac{3x}{13x} \times 100\%$$
$$=\dfrac{3}{13} \times 100\%$$
$$=\dfrac{300}{13} \%$$
$$=23\dfrac{1}{13} \%$$
Therefore we can say that B’s salary is less than that of A’s by $$23\dfrac{1}{13} \%$$.
Hence the correct option is option C.

Note: To solve this type of question you need to know whether you have been given to find the change in B w.r.t A then you have to divide their difference by A, i.e, $$\dfrac{B-A}{A}$$(if B > A) or $$\dfrac{A-B}{A}$$ (if A > B), and to find percentage you have to multiply the above term with 100%.