- Home
- Standard 13
- Quantitative Aptitude
Savita buys $5$ shirts and $10$ pants for $Rs.$ $1600 .$ She sells shirts at a profit of $15 \%$ and pants at a loss of $10 \% .$ If her over all profit was $Rs.\,90$ what was the cost price of a shirt and a pant in $Rs.$?
$175,50$
$200,50$
$200,60$
Cannot be determined
Solution
Let $Rs.\, p$ be the cost price of a shirt and $Rs.$ $q$ be the cost price of a pant. Then,
$CP$ of $5$ shirts $=$ Rs. $5 p$
$CP$ of $10$ pants $=$ Rs. $10 q$
$\therefore \quad 5 p+10 q=1600$ $…(i)$
Profit on the sale of $5$ shirts $=\frac{15 \times 5 p }{100}= Rs \cdot \frac{3 p }{4}$
Loss on the sale of $10$ pants $=\frac{10 q \times 10}{100}= Rs . q$
Given,
Profit on the shirts $-$ Loss on pants $=$ $Rs. 90$
$\Rightarrow \quad \frac{3 p}{4}-q=90$
$\therefore \quad 3 p-4 q=360$ $…(ii)$
Multiplying $(i)$ by $3$ and $(ii)$ by $5$ and then subtracting $(ii)$ from $(i),$ we get
$50 q =3000 \Rightarrow q =\frac{3000}{50}= Rs .60$
Puting the value of $q$ in $(i)$ we get
$5 p=1000 \Rightarrow p=\frac{1000}{5}=$ $Rs. 200$
Hence, the cost price of shirt is $Rs. 200$ each and the cost price of pant is $Rs. 60$ each.
