Question

If a harmonium is sold for Rs. 16 , the percentage of loss is equal to its cost price. Find out the cost price of the harmonium.

Answer 1

Hint: We can do this question by using a percentage loss formula because we have given a percentage loss equal to the cost price of harmonium.
$\text{Percentage}\,\text{Loss}\,\text{=}\,\dfrac{\text{Loss}}{\text{Cost}\,\text{Price}}\text{ }\!\!\times\!\!\text{ 100}$
We can find Loss by subtracting cost price and selling price.

Complete step by step solution:
The cost price of Harmonium is Rs. X.
Selling price of Harmonium is Rs.16
Hence Loss = Cost price – Selling Price = X-16
As we know formula for percentage loss as below
$\Rightarrow \text{Percentage}\,\text{Loss}\,\text{=}\,\dfrac{\text{Loss}}{\text{Cost}\,\text{Price}}\text{ }\!\!\times\!\!\text{ 100}$
$\Rightarrow \text{Percentage}\,\text{Loss}=\dfrac{X-16}{X}\times 100$
As given percentage loss equal to cost price.
So we can write
$\Rightarrow \dfrac{X-16}{X}\times 100=X$
$\Rightarrow 100X-1600={{X}^{2}}$
$\Rightarrow {{X}^{2}}-100X+1600=0$
We can factorize it by splitting the middle term in such two parts whose summation is equal to the middle term and multiplication is equal to the product of the first and last term of the equation.
In above equation product of first and last term is ${{X}^{2}}\times 1600=1600{{X}^{2}}$
So we need to split the middle term i.e $100X$ in such two parts whose summation is equal to$-100X$ middle term and multiplication is equal to $1600{{X}^{2}}$.
 $\Rightarrow {{X}^{2}}-80X-20X+1600=0$
$\Rightarrow X(X-80)-20(X-80)=0$
$\Rightarrow (X-80)(X-20)=0$
Either $(X-80)=0$ or $(X-20)=0$
$X=80$ or $X=20$
Hence cost price of Harmonium is Rs. 80 or Rs. 20
Note: We need to be careful about the percentage loss formula. As we have percentage loss equal to cost price it means we need to write cost price as it is equal to percentage loss because we already multiplied 100 in percentage loss formula.
And when we will multiply 100 in (X-16) we will multiply it in both X and 16.