Question

A vendor bought $20$ oranges for Rs $56$ and sold them at Rs $35$ per dozen. If his gain or loss percent is given by $\frac{p}{q}\%$, where $p$ and $q$ are co-primes, then find the value of $p-q$.

Answer 1

Let the number of oranges bought $=$ LCM of $20$ and $12=60$. $\because$ he sold in dozens i.e, in multiples of $12$

C.P. of $20$ oranges $=$ Rs.$56$

$\therefore$ C.P. of $1$ orange $=$ Rs. $\frac{56}{20}$
Hence the C.P. of $60$ oranges $=$ Rs.$(\frac{56}{20}\times 60)=$ Rs. $168$
S.P. of $12$ oranges $=$ Rs. $35$

$\therefore$ S.P. of $1$ orange $=$ Rs. $\frac{35}{12}$
Hence, the S.P. of $60$ oranges $=$ $(\frac{35}{12}\times 60)=Rs.175$

Thus C.P. $=$ Rs.168 and S.P. $=$ Rs. $175$
Since (S.P.) $>$ (C.P.) So, the vendor has made a gain
Gain $=(175-168)=$ Rs. $7$

$\therefore$ Gain $\%$ $=$ $(\frac{Gain}{C.P.}\times 100)\%=(\frac{7}{168}\times 100)\%=\frac{25}{6}\%$

We can see that, $p=25$ and $q=6$ and both are coprimes

Thus, $p-q=25-6=19$