Word Problem10:

Word Problem10: A horse is sold for Rs 1230 at a loss of 18%. What would have been gained or lost percent if it had been sold for Rs 1600 ?

a. 6-2/3% gain                b.  7% loss              c. 8% gain               d. 9-1/2% loss

Solution:

Here we suppose that cost price

CP= y

Now first sale price is Rs 1230 i-e

SP1 = 1230

and

Loss = 18 % of CP = 18/100\times y=18y/100

But

loss= CP-SP1

Putting values of Loss, CP and SP1

\Rightarrow \frac{18y}{100}=y-1230

Simplifying gives us;

\frac{9y}{50}-y=-1230

\frac{9y-50y}{50}=-1230

\frac{-41y}{50}=-1230

\Rightarrow y=\frac{1230\times50}{41}=30\times50=1500

So cost price  is Rs 1500

i-e CP=1500

Now had it been sold for Rs 1600, then we see it would have gain of Rs 100 !

i-e Profit = P = 100

Now to find what percentage it (the profit of 100 rupees) makes of cost price, we suppose that it makes ‘x’ [ercent of CP !

i-e

P=x/100 of CP

\Rightarrow 100=\frac{x}{100}\times 1500

\Rightarrow x=\frac{100\times100}{1500}

\Rightarrow x=6-\frac{2}{3}%

So the option ‘a’ is the answer

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