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Question

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(a) 26.36%

(b) 16.67%

(c) 9.09%

(d) 27.27%

Answer

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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%.

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