Question

Question 13
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.

Answer 1

Let the number of bananas in lots A and B be x and y respectively
Case I: Cost of the first lot at the rate of Rs. 2 for 3 bananas + Cost of the second lot at the rate
Of Rs.1 per banana = amount received
$\Rightarrow \frac{2}{3}x+y=400$
$\Rightarrow 2x+3y=1200$ ...(i)
Case II: Cost of the first lot at the rate of Rs.1 per banana and the second lot at the rate of Rs. 4 for 5 bananas = amount received
$\Rightarrow x+\frac{4}{5}y=460$
$\Rightarrow$ $5x+4y=2300$ ...(ii)

On multiplying Eq. (i) by 4 and Eq (ii) by 3 and then subtracting them, we get

8x + 12y = 4800

15x + 12y = 6900

-7x = - 2100

x = 300

Now, put the value of $x$ in Eq (i) we get

2 $\times$ 300 + 3y = 1200

$\Rightarrow$ 600 + 3y = 1200

$\Rightarrow$ 3y = 1200 – 600

$\Rightarrow$ 3y = 600

$\Rightarrow$ y = 200

$\therefore$ Total number of bananas = Number of bananas in lot A + Number of bananas in lot B = x + y

= 300 + 200 = 500

Hence, he had 500 bananas.