Word Problem 17

Problem 17: A watch was sold at a loss of 10%. If it were sold for Rs 10 more, there would have been a gain of 10%. Find for how much the watch was sold.

a. Rs 45             b. Rs 40                      c. Rs 30                        d. Rs 60

GRE arithmetic questions and answers

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Solution:

Let Cost price of the watch is ‘y’ i-e

CP=y

Given it was sold at 10% loss of CP

 L=\frac{10y}{100}

we know formula for loss;

L= CP-SP

\Rightarrow SP=CP-L

\Rightarrow SP=y-\frac{10y}{100}

\Rightarrow SP=\frac{90y}{100}

So this is the sale price for given information !

if the watch was sold for Rs 10 more, then sale price would have been

 sp=\frac{90y}{100}+10

And it is said that there would have been a profit of 10% of CP i-e

p=\frac{10y}{100}

Now use formula for profit

p=sp-CP

put values

\frac{10y}{100}=(\frac{90y}{100}+10)-y

 \Rightarrow y+\frac{10y}{100}=\frac{90y}{100}+10

 \Rightarrow \frac{110y}{100}=\frac{90y}{100}+10

 \Rightarrow \frac{20y}{100}=10

 \Rightarrow y=50

So cost price of the watch  CP was Rs 50

put this value of y in ;

\Rightarrow SP=\frac{90y}{100}

 \Rightarrow SP=\frac{90\times 50}{100}=45

So, the watch was sold for Rs 45

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