Question

The ratio of two numbers is 4 : 5, but if each number is increased by 20, the ratio becomes 6 : 7. The sum of such number is:
A. 90
B. 95
C. 100
D. 60

Answer 1

Hint: For solving this type of question you should know about the ratio of two numbers and variation in the values with the increment and decrement of the values by a constant or any digit. In this question the ratio of both will change with the increment of each number by 20. And with the increment, the ratio will also vary.

Complete step-by-step solution:
Here according to the question, the ratio of two numbers is given as 4 : 5. Let us assume that the numbers are 4x and 5x. So, according to the question, the ratio of 4x and 5x is 4 : 5, that is,
$\dfrac{4x}{5x}=\dfrac{4}{5}$
And after we increase the numbers by 20, the numbers will become $4x+20$ and $5x+20$ and the ratio of the numbers becomes 6 : 7 now. So, we can write it as,
$\dfrac{4x+20}{5x+20}=\dfrac{6}{7}$
By solving this equation, we will get,
$28x+140=30x+120$
By taking all the x terms to left side and the others to the right side, we will get,
$\begin{align}
  & 28x-30x=120-140 \\
 & \Rightarrow -2x=-20 \\
 & \Rightarrow x=10 \\
\end{align}$
So, here we get the value of x as 10.
Now we have to calculate the sum of the given numbers. To calculate the sum, we will do,
Sum $=4x+5x$ and since $x=10$, so sum will be,
$\begin{align}
  & 4\left( 10 \right)+5\left( 10 \right) \\
 & \Rightarrow 40+50 \\
 & =90 \\
\end{align}$
So, the sum of the numbers is 90.
Hence the correct option is A.

Note: While solving this question you should be careful calculating the value of x. This is so because after increment and decrement it is necessary to apply the increment and decrement in the equation and then calculate it with the help of the ratio of new numbers which are generated by applying the increment.