Question

Raju sells cement at a profit of 10%. Had he bought at 10% less and sold it for Rs. 20 less, he would have gained 20 %. Then what is the cost price of the cement?​

Answer 1

Solution:-

♦ Let CP be Rs.x

Gain% = 10%

So, Gain = 10% of x = x/10

So, SP = CP + Gain

→x+x/10

→10x+x/10

→Rs. 11x/10

Now, New CP = x - 10% of x

→x-x/10

→9x/10

Now, Gain = 20%

So,

New SP =

$\begin{gathered} \longrightarrow \rm \bigg \{ \frac{(100 + gain\% \times \: CP }{100} \bigg \} \\ \longrightarrow \rm \frac{120}{100} \times \frac{9x}{10} \\ \longrightarrow \rm \frac{108x}{100} \end{gathered}$

It is given that SP become 20 less

So,

$\begin{gathered} \leadsto \rm \: \frac{11x}{10} - \frac{108x}{100} = 20 \\ \leadsto \rm110x - 108x = 2000 \\ \leadsto \rm2x = 2000 \\ \leadsto \rm \: x = \cancel \frac{2000}{2} \\ \leadsto \rm \: x = 1000\end{gathered}$

So, CP = Rs. 1000