Question

29) A shopkeeper sells a pair of sunglasses at a
profit of 25%. If he had bought it at 25% less
and sold it for Rs 10 less, then he would have
gained 40%. The cost price of the pair of
sunglasses is :​

Answer 1

Answer :-

• CP of the pair of sunglasses is 50.

Given :-

• On selling a pair of sunglasses a shopkeeper had gained 25%.
• If he had bought it at 25% less
• and sold it for Rs 10 less, Then he would gain 40%.

To find :-

• Cost price of pair of sunglasses?

Step by step explanation :-

Detailed explanation of solution :-

Let's understand!

A shopkeeper sold a pair of sunglasses at profit of 25%. Also given that, If he would sold it for 25% less and then sold it for Rs. 10 less. He would have gained 40%.

We are asked to find CP of the pair of sunglasses.

How to solve ?

We will calculate SP of sunglasses when he had 25% profit. And then, CP of sunglasses If he had bought it at 25% less and sold it for Rs 10 less. Then, SP of sunglasses If he had bought it at 25% less and sold it for Rs 10 less.

At last, There is a formula - SP = Gain% × CP.

• We will use that, To find CP (x) .

Now, Let's do it !

Calculations :-

Let CP of sunglasses be x

SP of sunglasses when shopkeeper gained 25% :-

$\implies \sf \dfrac{x \times 125}{100}$

• 100 + 25 = 125.

On simplifying,

$\implies \sf \dfrac{x \times 5}{4}$

$\implies \sf \dfrac{5x}{4}$

Thus, CP = 5x/4

CP of sunglasses If he had bought it at 25% less :-

$\implies \sf \dfrac{75}{100} \times x$

• 100 - 25% = 75. As it is, 25% less we need to subtract.

On simplifying,

$\implies \sf \dfrac{3}{4} \times x$

$\implies \sf \dfrac{3x}{4}$

So, CP = 3x/4

Now, SP of sunglasses If he had sold it for Rs 10 less :-

Applying this, SP = CP - discount,

$\implies \sf \dfrac{5x}{4} - 10$

• We know that, CP = 5x/4.
• If he had sold it for Rs 10 less. So, (-)

It can't be further simplified.

So, SP = 5x/4 - 10.

Given that,

• he would have gained 40%. If he had bought it at 25% less and sold it for Rs 10 less.

SP = Gain % × CP.

• Here, Gain % = 40%.

Now, Applying this,

$\implies \sf \dfrac{5x}{4} - 10 = \dfrac{140}{100} \times \dfrac{3x}{4}$

• 100 + 40 = 140.

On simplifying,

$\implies \sf \dfrac{5x}{4} - 10 = \dfrac{420x}{400}$

$\implies \sf \dfrac{5x}{4} - 10 = \dfrac{21x}{20}$

Transposing 21x/20 from RHS to LHS Changing sign from (+) to (-) and transposing - 10 from LHS to RHS, Changing sign from (-) to (+).

Therefore, we get :-

$\implies \sf \dfrac{5x}{4} - \dfrac{21x}{20} = 10$

$\implies \sf \dfrac{5x \times 5 - 21x \times1 }{20} = 10$

On simplifying,

$\implies \sf \dfrac{25x- 21x }{20} = 10$

Subtracting 21x from 25x,

$\implies \sf \dfrac{1x }{5} = 10$

Transposing 5 from LHS to RHS, Changing sign,

$\implies \sf x = 10 \times 5$

Multiplying 10 with 5,

$\implies \sf x = 50$

Therefore, CP of the pair of sunglasses is 50.

Answer 2

$\huge \sf \purple{Solution - : }$

$\sf{Let \: the \: C.P. \: of \: sunglasses \: will \: be \: x}$

Then S.P. = 100x125x= Rs. 45x

$\sf{New C.P. = Rs.\frac{5x}{4} - 10= Rs. \frac{140}{100} \times{3x}{4}</p><p>}$

$\sf{New \: S.P. = Rs.( \frac{5x}{4} - 10)}$

$\sf{\frac{5x}{4} -\frac{21x}{20} = 10</p><p>}$

$\sf{\frac{25x−21x}{20}=10}$

$\sf{⇒4x=200}$

$\sf{⇒x= Rs. 50}$