Question

Raj had oranges and he divided them into Set A and Set B. He sold the first set at the rate of Rs.3 for 4 oranges and the second set at Rs.1 per orange and got a total of Rs.510. If he had sold the first set at the rate of Rs.1 per orange and the second set at the rate of Rs.5 for 6 oranges, his total collection would have been Rs.560. Find the total number of oranges he had.​

Answer 1

❥︎Question :-

• Raj had oranges and he divided them into Set A and Set B. He sold the first set at the rate of Rs.3 for 4 oranges and the second set at Rs.1 per orange and got a total of Rs.510. If he had sold the first set at the rate of Rs.1 per orange and the second set at the rate of Rs.5 for 6 oranges, his total collection would have been Rs.560. Find the total number of oranges he had.

❥︎Solution :-

Let number of Oranges in Set A be 'x' and number of Oranges in Set B be 'y'.

❥︎Case :- 1

He sold the first set at the rate of Rs.3 for 4 oranges and the second set at Rs.1 per orange and got a total of Rs.510.

For set A

Selling Price of 4 oranges = Rs 3

Selling Price of x oranges = Rs 3x/4

For Set B

Selling Price of 1 orange = Rs 1

Selling Price of y oranges = Rs y.

According to the statement,

$\bf\implies \:\dfrac{3x}{4} + y = 510$

$\bf\implies \:3x + 4y = 2040.....(1)$

❥︎Case :- 2

He had sold the first set at the rate of Rs.1 per orange and the second set at the rate of Rs.5 for 6 oranges, his total collection would have been Rs.560.

For Set A

Selling Price of 1 orange = Rs 1

Selling Price of x oranges = Rs x.

For Set B

Selling Price of 6 oranges = Rs 5

Selling Price of y oranges = Rs 5y/6

According to the statement

$\bf\implies \:x + \dfrac{5y}{6} = 560$

$\bf\implies \:6x + 5y = 3360.....(2)$

Multiply (1) by 2 and subtract (2) from it, we get

$\bf\implies \:6x + 8y - 6x - 5y = 4080 - 3360$

$\bf\implies \:3y = 720$

$\bf\implies \:y = 240$

Put y = 240 in equation (1), we get

$\bf\implies \:3x + 4 \times 240 = 2040$

$\bf\implies \:3x + 960 = 2040$

$\bf\implies \:3x = 1080$

$\bf\implies \:x = 360$

$\bf\implies \:total \: number \: of \: oranges = x + y$

$\bf\implies \:240 + 360 = 600$