Question

A motorcycle was sold at a 20 % profit for Rs. 40,000. Its cost price is:
(a) \[Rs.40000\times \dfrac{100}{120}\]
(b) \[Rs.40000\times \dfrac{120}{100}\]
(c) \[Rs.40000\times \dfrac{80}{100}\]
(d) \[Rs.40000\times \dfrac{100}{80}\]

Answer 1

Hint: First of all write the formula of profit % that is \[\text{Profit %}=\dfrac{\left( S.P-C.P \right)}{C.P}\times 100\]. Now, substitute the values of profit % and S.P in this formula and solve it to get the value of C.P.

Complete step-by-step answer:

Here, we are given that the motorcycle is sold at 20 % profit for Rs. 40,000. We have to find its cost price. The profit and profit % is given by:
Profit = Selling Price (S.P) – Cost Price (C.P).
\[\text{Profit %}=\dfrac{\left( S.P-C.P \right)}{C.P}\times 100\]
Or,
\[\text{Profit %}=\dfrac{\text{Profit}}{C.P}\times 100\]
Now, let us consider our question. Here we are given that the motorcycle is sold at 20 % profit for Rs. 40000. So, we get,
Selling Price (S.P) of motorcycle = Rs. 40,000.
Profit % on selling motorcycle = 20 %.
We know that, \[\text{Profit %}=\dfrac{\left( S.P-C.P \right)}{C.P}\times 100\]
So, by substituting the value of profit % = 20 % and S.P = Rs.40000 in the above equation, we get,
\[20=\left( \dfrac{40000-C.P}{C.P} \right)\times 100\]
By dividing 100 on both the sides of the above equation, we get,
\[\dfrac{20}{100}=\left( \dfrac{40000-C.P}{C.P} \right)\]
We can also write the above equation as,
\[\dfrac{40000}{C.P}-\dfrac{C.P}{C.P}=\dfrac{20}{100}\]
\[\Rightarrow \dfrac{40000}{C.P}-1=\dfrac{20}{100}\]
By adding 1 on both the sides of the above equation, we get,
\[\Rightarrow \dfrac{40000}{C.P}=\dfrac{20}{100}+1\]
\[\Rightarrow \dfrac{40000}{C.P}=\dfrac{120}{100}\]
By cross multiplying the above equation, we get,
\[100\times 40000=120\times C.P\]
By dividing 120 on both the sides, we get,
\[C.P=40000\times \dfrac{100}{120}\]
So, we get the cost price as \[Rs.40000\times \dfrac{100}{120}\].
Hence, option (a) is the right answer.

Note: In questions related to cost price, selling price, profit, etc. students often get confused while remembering the formulas of C.P, S.P, Profit, etc. individually. So, apart from learning multiple formulas and getting confused, students should remember only one formula, that is \[\text{Profit %}=\dfrac{\left( S.P-C.P \right)}{C.P}\times 100\] , and substitute in it the given values to find the unknown value.