Question

A shopkeeper sold two watches for Rs.425 each, gaining 10% on one and losing 10% on the other. Then he
A.Neither gains nor loss
B.Gains 1%
C.Loses 1%
D.None

Answer 1

Hint: First by using profit, loss find the cost price of both the watches. As we know the total selling price will be 2 multiplied by a given number. Add the both cost prices we get. Now by using total cost price, total selling price. Find the value of profit or loss suffered by the shopkeeper.

Complete step-by-step answer:
Given the cost at which he sold is written in the form:
Selling price of watches = RS.425 each
Let the first watch be represented by the variable A.
let the second watch be represented by the variable B.
Case I: Solving the case for selling the watch A.
Given conditions on the selling process of watch A are:
Selling price of watch A = Rs.425
Profit gained on watch A = 10%
So, the relation between profit P, Selling price S.P, Cost price C.P is:
\[\dfrac{{100 + P}}{{100}} \times CP = SP\]
By substituting the values, by assuming Selling price as S.P is:
\[\dfrac{{100 + P}}{{100}} \times CP = 425\]
By cross multiplying, we get the equation of C.P as below:
\[\left( {110} \right)CP = 42500\]
By dividing with 110 on both sides of equation, we get it as:
\[CP = \dfrac{{42500}}{{110}}\]
By simplifying the above equation, we can say the value of CP as:
\[CP = Rs.386.36\] ……………..(1)

Case II: Solving the case for selling the watch B.
Given conditions on selling price of watch B, are written as:
Selling price of watch B \[ = Rs.425\], loss on watch is \[ = 10\% \]
The relation between loss l, selling price SP, cost price CP, is:
\[\dfrac{{100 - l}}{{100}} \times CP = 425\]
Let the value of CP of B be cp, by substituting all the values, we get:
\[\dfrac{{100 - 10}}{{100}} \times cp = 425\]
By cross multiplying, we get value of cp as:
\[\left( {90} \right)cp = 42500\]
By dividing with 90 on both sides of equation, we get:
\[cp = \dfrac{{42500}}{{90}} = 472.22{\rm{ }}\] ……………..(2)
Total Cost price can be found, as below equation:
\[Total{\rm{ Cost}}\,\,{\rm{Price = CP + cp}}\]
From equation (1), (2) we get total CP \[ = 386.36 + 472.22\]
\[Total{\rm{ Cost}}\,\,{\rm{Price = 858}}{\rm{.58 }}\] ……………..(3)
Total Selling Price can be found by,
\[Total{\rm{ Selling Price = 2}} \times {\rm{425 = 850 }}\] …………..(4)
Total Cost Price > Total Selling Price \[ \Rightarrow \]Loss occurred
Loss can be found by relation:
\[\dfrac{{CP - SP}}{{CP}} \times 100\]
By substituting equation (3), (4), we get loss value as:
\[Loss = \dfrac{{858.58 - 850}}{{858.58}} \times 100{\rm{ = }}\dfrac{{8.58}}{{858.58}} \times 100{\rm{ = 1\% }}\]
Therefore, the shopkeeper has 1% loss.
Option (c) is correct.

Note: Be careful, generally students think 10% profit, 10% loss implies neither profit nor loss. But, here we have two different items. There is a possibility of different Cost prices. So, we get different gains, losses. So, you must not conclude by saying always solve each and every step to reach the result.