Ravipurchases 90 pens and sells 40 pens at a gain of 10 % and 50 pens at a gain of 20 % . Had he sol

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Gujarati

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7.Profit and Loss

hard

Ravipurchases $90$ pens and sells $40$ pens at a gain of $10 \%$ and $50$ pens at a gain of $20 \% .$ Had he sold all of them at a uniform profit of $15 \%$ he would have got $Rs.\, 40$ less. Find the cost price of each pen in $Rs.$

$80$

$75$

$90$

$100$

Let the $CP$ of each pen be $Rs. 100$

At the profit of $10 \%,$ $SP$ of $40$ pens $=(100+10) \times 40=$ $Rs. 4400$

At the profit of $20 \%,$ $SP$ of $50$ pens $=(100+20) \times 50=$ $Rs. 6000$

$SP$ of $90$ pens $=$ Rs. $(4400+6000)=$ $Rs. 10400$

$CP$ of $90$ pens $=$ $Rs.$ $(90 \times 100)=$ $Rs. 9000$

At the profit of $15 \%,$ $SP$ of $90$ pens $=$ $Rs.$ $(90 \times 115)=$ $Rs. 10350$

Difference in $SP =$ $Rs.$ $(10400-10350)=$ $Rs. 50$

If the difference is Rs. $50,$ then $C P=R s .100$

If the difference is Rs. $40,$ then $CP$

$=\frac{100 \times 40}{50}=$ $Rs. 80$

Hence, the cost price of each pen is $Rs. 80$

Standard 13

Quantitative Aptitude

medium

medium

hard

medium

easy