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Abhinav bought some pencils in ₹ X. He sold 20% of pencils at 25% loss, one third at 20% profit and the remaining at 25% profit. If the total profit e
Question

Abhinav bought some pencils in ₹ X. He sold 20% of pencils at 25% loss, one third at 20% profit and the remaining at 25% profit. If the total profit earned by him on selling all the pencils is ₹ 248, then find the value of X (in ₹).

A.

1450

B.

1680

C.

1750

D.

1860

Correct option is D

Given:

Total cost price of all pencils = X

Sold: 20% at 25% loss,13\frac{1}{3}​ at 20% profit, remaining at 25% profit

Total profit = ₹248

Formula Used:

Profit amount=(Overall profit %)×X = (\text{Overall profit \%})\times X​​

Solution:
Shares by quantity: 0.20,13,10.2013=715.0, \frac{1}{3}, 1-0.20-\frac{1}{3}=\frac{7}{15}.​​

Overall profit (%):
0.20(25%)+13(20%)+715(25%)20(-25\%) + \frac{1}{3}(20\%) + \frac{7}{15}(25\%)​​
=5%+(623%)+(1123%)= -5\% + (6\frac{2}{3}\%) + (11\frac{2}{3}\%)​​

=1313%=215= 13\frac{1}{3}\% = \frac{2}{15}​​
Thus,
215X=248 X=248×152=1,860.\frac{2}{15}X = 248 \implies X = 248\times\frac{15}{2} = ₹1,860.​​
​​

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