Question

If $?\%\text{ of }400+31\%\text{ of }600=50\%\text{ of }820$ , find the missing number.
$\begin{align}
  & \text{A}\text{. }52 \\
 & \text{B}\text{. }56 \\
 & \text{C}\text{. }64 \\
 & \text{D}\text{. }36 \\
\end{align}$

Answer 1

Hint: To find the missing number first we need to assume the missing number as ‘x’. Then we can find the percentage of terms on the RHS and LHS separately. After that, we will get simpler terms and a linear equation in one variable, i.e x. We can then simplify it to get the missing number.

Complete step by step solution:
Here in this it is given that $?\%\text{ of }400+31\%\text{ of }600=50\%\text{ of }820$.
To find the missing number, let us assume ‘x’ as the missing number.
We know that $1\%=\dfrac{1}{100}$ , by this we get –
$\dfrac{x}{100}\times 400+\dfrac{31}{100}\times 600=\dfrac{50}{100}\times 820$
$\Rightarrow \dfrac{400x}{100}+\dfrac{18600}{100}=\dfrac{41000}{100}$
By simplifying the above equation, we get –
$4x+186=410$
By subtracting 186 on both sides, we get –
$4x=410-186$
$\Rightarrow 4x=224$
By dividing ‘4’ on both sides, we get –
$x=56$
Therefore, the missing number is 56.
Hence option (B) is the correct answer.

Note: Students can check the answer we get is correct.
Here we will take the answer and check whether R.H.S is equal to L.H.S to check our answer.
$56\%\text{ of }400+31\%\text{ of }600=50\%\text{ of }820$
We can write it as –
$\dfrac{56}{100}\times 400+\dfrac{31}{100}\times 600=\dfrac{50}{100}\times 820$
By simplifying we get –
$56\times 4+31\times 6=5\times 82$
$\begin{align}
  & \Rightarrow 224+186=410 \\
 & \Rightarrow 410=410 \\
\end{align}$
Hence proved L.H.S is equal to R.H.S. So, our answer is correct.