Question

If the cost of bananas is increased by Rs.$10$ per dozen, one can get $3$ dozen less for Rs.$600$. Find the original cost of one dozen of bananas.

Answer 1

Let the number of dozens of bananas be $x$

Let the original cost of bananas be $c$

Given that $(c+10)(x-3)=600$ and $xc=600$

$\Rightarrow xc+10x-3c-30=600$ and $xc=600$

$\Rightarrow 10x=3c+30$

From $xc=600$ , we get $x=\frac{600}{c}$

By substituting , we get $\frac{6000}{c}=3(c+10)$

$\Rightarrow c+10=\frac{2000}{c}$

Observe that $c=40$ will satisfy the above condition

Therefore the original cost is $40Rs$