Question

A gets 10% more than B. Then B gets
(a) 10% more than A
(b) 10% less than A
(c) \[9\dfrac{1}{11}\]% more than A
(d) none of these

Answer 1

Hint: In this question, we need to find the 10% of B and then add it to B using the percentage formula which is given by \[\dfrac{x}{100}\times y\]. Then, we need to add this percentage value of B to B and then equate it to A. Now, we need to simply further and write the value of A in terms of B to get the final result.

Complete step by step answer:
The word 'percent' means 'per hundred' or 'out of hundred', symbol % is used to express percentage.
The percentage can be converted into fraction, by dividing the percentage by 100.
If percentage is a%, then its fraction will be \[\dfrac{a}{100}\]
Now, given that A is 10% more than B.
Let's find the value of 10% of B
As we already know from the percentage formula that
  \[\dfrac{x}{100}\times y\]
Now, using the above formula we get the value of 10% of B as
\[\Rightarrow \dfrac{10}{100}\times B\]
Now, this can be further written in the simplified form as
\[\Rightarrow 0.1B\]
Here, given that A is 10% more than B which can be further written as
\[\Rightarrow A=B+0.1B\]
Now, on simplifying this further we get,
\[\Rightarrow A=1.1B\]
Let's now write the value of B in terms of A by rearranging the terms
\[\Rightarrow B=\dfrac{A}{1.1}\]
Now, on simplifying this further we get,
\[\Rightarrow B=0.91A\]
Now, this can also be written in other form as
\[\Rightarrow B=A-0.09A\]
Now, this can be further written as
\[\Rightarrow B=A-\dfrac{9}{100}A\]
Thus, B gets 9% less than A.

So, the correct answer is “Option d”.

Note: Instead of writing A in terms of B from the given condition and then further converting b in terms of A we can also find it by assuming A as some value and then write the value of B accordingly which on further simplification gives the relation between them.
It is important to note that we cannot directly say that B has 10% less than A as A has 10% more than B. Because the percentage value can be equal on both the sides but the value being increased and decreased cannot be equal directly.