Question

Vijay had some bananas, and he divided them into two lots $A$ and $B$. He sold the first lot at the rate of Rs. $2$ for $3$ bananas and the second lot at the rate of Rs. $1$ per banana, and got a total of Rs. $400$. If he had sold the first lot at the rate of Rs. $1$ per banana, and the second lot at the rate of Rs. $4$ for $5$ bananas, his total collection would have been Rs. $460$. Find the total number of bananas he had.

• A. $200$
• B. $500$
• C. $600$
• D. $900$

Answer 1

The correct option is B $500$

Let the first lot $=x$ and the second lot $=y$, both in Rs .

$\therefore$ total number of bananas $=x+y$

In the first case price of $x$ bananas at the rate of Rs. $2$ per $3$ bananas $=\frac{2x}{3}$ and price of $y$ bananas at the rate of Rs. $1$ per banana $=y$.

$\therefore$ by the given condition $\frac{2x}{3}+y=400$

$\Rightarrow 2x+3y=1200$ ..............(i)

In the second case price of $x$ bananas at the rate of Rs. $1$ per banana $=x$ and price of $y$ bananas at the rate of Rs. $4$ per $5$ banana $=\frac{4}{5}y$

$\therefore$ by the given condition $x+\frac{4}{5}y=460$

$\Rightarrow 5x+4y=2300$ ........(ii)

Multiplying (i) by $5$ and (ii) by $2$, we get

$10x+15y=6000$ ........(iii) and $10x+8y=4600$ .........(iv)

Subtracting (iv) from (iii), we get

$7y=1400$

$\Rightarrow y=200$

Putting $y=200$ in (i), we get

$2x+3\times 200=1200$

$\Rightarrow x=300$

$\therefore x+y=300+200=500$

So, Vijay had $500$ bananas.