Question

# If there are two numbers A and B and A is 20% more than B, then find by what percent B is less than A?(a) 26.36%(b) 16.67%(c) 9.09%(d) 27.27%

Hint: We start solving the problem by writing the actual relation between the value of A and value of B. We now solve for the rate at which the value of B is less than the value of A. Once we find this relation between B and A, we convert the value into the value of A in terms of percentage. We get the required value by subtracting the obtained percentage with 100.

Given that we have two numbers A and B. It is also said that the value of A is 20% more than the value of B. We need to find by what percentage the value of B is less than the value of A.
According to the problem, the value of A is 20% more than the value of B.
So, we have got the value of A = (100% + 20%) of the value of B.
We have got the value of A = 120% of the value of B.
We know that x% of y is $\dfrac{x}{100}$ of y.
So, we have got the value of A = $\dfrac{120}{100}\times$ the value of B.
We have got the value of A = $1.2\times$ the value of B.
Now, we find the value of B in terms of the value of A.
So, we have got the value of B = $\dfrac{1}{1.2}\times$ the value of A.
We have got the value of B = $0.8333\times$ the value of A.
We know that to convert any fraction into percentage, we multiply the given fraction with 100.
So, we have got the value of B = $\left( 0.8333\times 100 \right)%$ of the value of A.
We have got the value of B = 83.33% of the value of A.
We know that if the value of ‘x’ is y% of the value of z and $y<100$, then ‘x’ is (100 – y) % less than the value of z.
So, the value of B is (100 – 83.33) % less than the value of A.
The value of B is 16.67% less than the value of A.
∴ The percent that B is less than A is 16.67%.

So, the correct answer is “Option B”.

Note: We should not directly say that the value of B is 20% less than the value of A as the result of division will not be the same in both cases. The examples to prove such types of differences are changes in foreign currency in their respective countries. We should not report the answer as 83.33% as the value of B is 83.33% of the value of A.