Question

A milkman sold two of his buffaloes for Rs.20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find out his overall gain or loss.

Answer 1

Hint: Since we have the selling price of the buffaloes, i.e. Rs.20,000 each, so we can find the cost price by the formula, $CP = \dfrac{{100}}{{100 + P\% }} \times S.P.$, when gain is there and the formula when loss is there then, $CP = \dfrac{{100}}{{100 - l\% }} \times S.P.$

Complete step-by-step answer:

We have been given in the question –

S.P. of each buffalo = Rs.20,000.

Gain % = 5%

Loss% = 10%.

Now, the milkman made a gain of 5% on selling one of his buffalo.

So, using the formula, $C{P_1} = \dfrac{{100}}{{100 + P\% }} \times S.P.$ to find the cost price.

Here, C.P1 is the cost price of the first buffalo, P is the gain, SP is the selling price.

Now, putting the values of S.P. of each buffalo = Rs.20,000, Gain %(P) = 5% in the formula we get-

$  C{P_1} = \dfrac{{100}}{{100 + 5}} \times 20,000 $

$   = \dfrac{{100}}{{105}} \times 20,000 $

$   = Rs.19047.62 $

Now, the milkman made a loss of 10% on selling the second buffalo.

So, using the formula, $C{P_2} = \dfrac{{100}}{{100 - l\% }} \times S.P.$ to find the cost price.

Here, C.P2 is the cost price of the first buffalo, P is the gain, SP is the selling price.

Now, putting the values of S.P. of each buffalo = Rs.20,000, loss %(l) = 10% in the formula we get-

$ C{P_2} = \dfrac{{100}}{{100 - 10}} \times 20,000 $

$   = \dfrac{{100}}{{90}} \times 20,000 $

$   = Rs.22,222.22 $

So, now the total cost price = $C{P_1} + C{P_2} = 19047.62 + 22222.22 = Rs.41269.84$

And the total selling price =$S{P_1} + S{P_2} = 20,000 + 20,000 = Rs.40,000$

Since, the C.P.>S.P., so there is a loss.

Overall Loss = C.P. – S.P.

Loss = C.P. - S.P. 

$   = 41269.84 - 40000 $

$   = Rs.1269.84 $

Hence, there is an overall loss of Rs. 1269.84.

Note: Whenever such types of questions appear, then always write down all the information given in the question, then by using the standard formulas of profit and loss find the values of cost price and selling price. Then, add up the total cost price and total selling price to find the overall gain or loss.