Question

if a sells an article to b at a profit of 20% b sells it to C at a loss of 4% what does it cost A if C has paid rupees 144​

Answer 1

A = Cost Price of A

B = Cost price of B

C = Cost price of C

B = Selling Price of A = A + (20÷100)A = A + 0.2A = 1.2A

C = Selling Price of B = B + (25÷100)B = B + 0.25B = 1.25B

Thus C = 1.25B = 1.25 × 1.2A = 1.5A = 225

Thus 1.5A = 225

Thus A = 225÷1.5

Thus A = 150 = Price at which A purchase the article.

Answer 2

In this question, the selling price at which 'A' sold it to be will be 'B's cost price.

And the price at which 'B' sold it to 'C' will be the selling price.

The amount would become 'C's cost price.

PRICE AT WHICH 'A' SELLS IT TO 'B'

$sp = \frac{100 + p\%}{100} \times cp$

$sp = \frac{120}{100} \times x$

$sp = \frac{120x}{100}$

by reducing it to the lowest terms, we get:

$\frac{6x}{5} = sp$

PRICE AT WHICH 'B' SELLS IT TO 'C' :

$sp = \frac{100 - l\%}{100} \times cp$

$sp = \frac{100 - 4}{100} \times ( \frac{6x}{5} )$

$sp = \frac{96}{100} \times \frac{6x}{5}$

by reducing to the lowest terms we get:

$sp = \frac{24}{25} \times \frac{6x}{5} = \frac{144x}{125}$

as it is already given that 'C' paid ₹144, it means that 'B' sold it to 'C' for ₹144

hence,

$\frac{144x}{125} = 144$

$144x = 144 \times 125$

$x = \frac{144 \times 125}{144}$

by cancelling, we get

x = ₹125

as we assumed that it costs 'A' ₹x.

Hope it helps

(NOTE : This might be a bit tricky to understand. Therefore if you still face any difficulty in understanding this explanation, please do post the question again I'll give a detailed answer)

Thank you!!

VERIFICATION:

$sp = \frac{6 \times 125}{5}$

by cancellation,

sp at which 'A' sold it = ₹ 150

'B' sold it at a loss of 4%

sp should be ₹144

$\frac{24}{25} \times 150$

by cancellation,

we get the answer as : 24 × 6 = ₹144

therefore, ₹144 = ₹144

hence verified.