Question

the cost price of two watches taken together is rupees 840 , if by selling one at a profit of 16% and the other at the loss of 12% , there is no gain or loss in the whole transaction then find the cost price of each watch .

Answer 1

ANSWER:-

Given:

The cost of price of two watches take together is Rs.840, If by selling one at profit of 16% and the other at the loss of 12%, there is no gain or loss in the whole transaction.

To find:

Find the cost price of each watch.

Solution:

Let the C.P. of first watch be Rs.x &

C.P.of the second watch= 840 -x

Therefore,

The first watch is sold at a profit of 16% and the second watch is sold at a loss of 12%.

So,

Selling price of first watch;

$= > x + \frac{16}{100} x \\ \\ = > \frac{100x + 16x}{100} \\ \\ = > \frac{116x}{100}$

Selling price of second watch;

$= > (840 - x) - \frac{12}{100} (840 - x) \\ \\ = > (840 - x)1 - \frac{12}{100} \\ \\ = > (840 - x) \frac{100 - 12}{100} \\ \\ = > (840 - x) \frac{88}{100}$

According to the question:

There is no gain or loss in the whole transaction.

Therefore,

S.P.= C.P.

$= > \frac{116}{100} x + \frac{88}{100} (840 - x) = 840 \\ \\ = > \frac{116x + 88 \times 840 - 88x}{100} = 840 \\ \\ = > 116x + 73920 - 88x = 84000 \\ \\ = > 28x = 84000 - 73920 \\ \\ = > 28x = 10080 \\ \\ = > x = \frac{10080}{28} \\ \\ = > x =Rs.360$

Therefore,

C.P. of first watch, x= Rs.360

C.P. of second watch, 840 -x

=) Rs.(840 - 360)

=) Rs.480

Hope it helps ☺️