Question

A house worth Rs.9000 is sold by Mr. A to Mr. B at a 10% loss Mr. B sells the house back to Mr. A at 10% gain. The result of the two transactions is
(a) Mr. S breaks even
(b) Mr. B gains Rs.900
(c) Mr. A losses Rs.900
(d) Mr. A losses Rs.810
(e) Mr. B gains Rs.1710

Answer 1

Hint: CP of the house is Rs.9000. Find the cost at which Mr. A sold it to Mr. B at 10% loss this becomes the new CP. Now find the cost at which Mr. B sells back at 10% gain. Now subtract this CP from other CP to find the loss of Mr. A.

Complete step by step solution:
Cost of the house = Rs.9000
It is said that Mr. A sold the house to Mr. B at 10%. Now let us find the price in which Mr. A sold the house to Mr. B.
10% loss = 10% of the cost price of the house.
 10% loss = \[\dfrac{10}{100}\times 9000=\] Rs.900.
\[\therefore \] Cost in which Mr. A sells house to Mr. B = CP of house – loss
\[\therefore \] Cost in which Mr. A sells house to Mr. B = 9000 – 900 = Rs.8100.
Hence we got the selling price of the house to Mr. B as Rs.8100.
Now let us find the rate at which Mr. B sells back the house to Mr. A. We have been told that Mr. B sells it back at 10% gain.
10% gain = 10% of the selling price of house to Mr. B.
10% gain = 10% of Rs. 8100 = \[\dfrac{10}{100}\times 8100\] = Rs.810.
\[\therefore \] Cost in which Mr. B sells the house back to A
= Rs.8100 + Gain of 10%
= 8100 + 810 = Rs.8910
\[\therefore \] Mr. B sells the house back to Mr. A at Rs.8910.
 Thus the loss for Mr. A again = 8910 – 8100 = Rs.810.
Hence Mr. A losses Rs.810
\[\therefore \] Option (d) is the correct answer.

Note: While Mr. B sells the house back to Mr. A, remember that the present CP of the house is Rs.8100 and not the original CP Rs.9000. You can compare the CP of Mr. A and Mr. B to know who has undergone the loss.