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word Problem 10

Profit & Loss 0

Problem 10: A man sold his watch at loss of 5%. He had sold it for Rs 56.25 more he would have gained 10%. Find the cost price of the watch.

a. Rs 300 b. Rs 375 c.Rs 400 d. Rs 200

Solution:

We suppose cost price as ‘y’

$CP=y$

Loss was 5% of CP

$L= \frac{5}{100}of CP$

$= \frac{1}{20}\times y$

$= \frac{y}{20}$

But fromula for loss is

$L=CP-SP$

$\frac{y}{20}=y-SP$

$\Rightarrow SP= y-\frac{y}{20}=\frac{19y}{20}$

So his sale price was 19y/20

Now come to the situation as wished in the question

If had he sold it with more 56.25 Rs then sale price would have been 19y/20+56.25 Rs

i-e

Wished sale price;

$SP= \frac{19y}{20}+56.25$

and in this case he would have earned profit of 10% of his CP

Wished profit;

$P=\frac{10}{100}of CP$

$P=\frac{y}{10}$

But formula for profit is

$P=SP-CP$

$\frac{y}{10}=\frac{19y}{20}+56.25-y$

$\frac{y}{10}=56.25-\frac{y}{20}$

$\frac{y}{10}+\frac{y}{20}=56.25$

$\Rightarrow\frac{3y}{20}=56.25$

$\Rightarrow y=\frac{20}{3}\times56.25$

$\Rightarrow y=375$

So, the cost price for the watch is Rs 375

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