Question

14. A carpenter undertakes to supply 2,000 tables
at Rs. 17.25 each. He estimates that if 10%
are defective which will be sold at 50%, then
the profit will be 15% on his whole outlay.
When the tables were supplied, 70% of the
tables were found defective. What loss did
carpenter incur?
(A) Rs. 7,800 (B) Rs. 16,075
(C) 4,666.25 (D) Rs. 6,075
(E) None of these​

Answer 1

Given:

Total no. of tables that the carpenter undertakes to supply = 2000

Cost of each table = Rs. 17.25

To find:

Loss incurred by the carpenter

Solution:

Calculations done on the basis of the estimation of the carpenter:

Carpenter estimates that 10% of the total no. of tables were defective

∴ No. of defective tables = 10% of 2000 = $\frac{10}{100} * 2000$ = 200

So, the remaining no. of non-defective tables = 2000 - 200 = 1800

Now,

The S.P. of non-defective tables = 1800 × 17.25 = Rs. 31050

and

200 defective tables were sold at 50% of the original price of each table

∴ S.P. of 200 tables = 200 × ½ × 17.25 = Rs. 1725

∴ The estimated S.P. of 2000 tables is given by,

= [ S.P. of non-defective tables ] + [ S.P. of defective tables ]

= [ Rs. 31050 ] + [ Rs. 1725 ]

= Rs. 32775

The carpenter estimated to have a profit of 15% on his whole outlay of Rs. 32775

∴ The estimated C.P. of the 2000 tables was,

= $\frac{100}{100 + 15} * 32775$ ........ [ Formula used: $C.P. = \frac{100}{100\: +\: Gain} * S.P.$ ]

= $\frac{100}{115} * 32775$

= Rs. 28500

Calculations done on the basis of actual scenario when the tables were supplied

Actually 70% of the tables supplied were found defective, so 30% of them will be non-defective.

∴ The actual S.P. of 2000 table was,

= [ S.P. of non-defective tables ] + [ S.P. of defective tables ]

= [ $\frac{30}{100}$ × 2000 × 17.25 ] + [ $\frac{70}{100}$ × 2000 × ½ × 17.25 ]

= [ Rs. 10350 ] + [ Rs. 12075 ]

= Rs. 22425

Calculating the loss incurred by the carpenter

Now, we will compare the estimated C.P. of the tables and the actual S.P. of 2000 tables, to find the loss incurred by the carpenter.

∴ Loss incurred by the carpenter is given by,

= [ Estimated C.P. ] - [ Actual S.P. ]

= [ Rs. 28500 ] - [ Rs. 22425 ]

= Rs. 6075

Thus, the loss incurred by the carpenter was Rs. 6075 ← option(D).

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