Question

Two numbers are less than a third number by 30% and 37% respectively. The percent by which the second number is less than the first is
A) 10
B) 7
C) 4
D) 3

Answer 1

Hint: Take 3 different numbers and use the relations between them. The Last number to be 100 this way it will be easy to determine the next 2 numbers and then we can easily find out the numbers we are told to.
Complete step by step answer:
Let us assume that the 3 numbers are A, B and C.
Now it is clear that A and B are less than C by thirty and thirty seven percent respectively.
Let us try to change C by 100. i.e., our third number is 100 now
We are given that A is 30% less than 100 and B is 37% less than 100
Now let us try to find out how much percent is B less than A
Now as C is 100
\[\begin{array}{l}
\therefore 30\% \times 100\\
 = \dfrac{{30}}{{100}} \times 100\\
 = 30
\end{array}\]
So it is clear that A is 30 less than 100
Clearly, \[A = 70\]
Now do the same thing for B
\[\begin{array}{l}
\therefore 37\% \times 100\\
 = \dfrac{{37}}{{100}} \times 100\\
 = 37
\end{array}\]
So B is 37 less than 100
Therefore B becomes 63
Now the difference between A and B is
\[\begin{array}{l}
 = A - B\\
 = 70 - 63\\
 = 7
\end{array}\]
Now we are down to how much percent is 7 of 70.
\[\begin{array}{l}
\therefore \dfrac{7}{{70}} \times 100\\
 = \dfrac{1}{{10}} \times 100\\
 = 10\%
\end{array}\]
So Option A is correct.

Note: Another way of doing this question could be that we can try to change A and B in the terms of C and then try to solve it using that A-B and finally get the values required. In both the cases we will get the same answer.