A fruit-seller sells 4 oranges for ₹ 3, gaining 50%. Find :

(i) C.P. of 4 oranges.

(ii) C.P. of one orange.

(iii) S.P. of one orange

(iv) profit made by selling one orange

(v) number of oranges need to be bought and sold in order to gain ₹ 24.

(i) Given:

S.P. of 4 oranges = ₹ 3

S.P. of 1 orange = ₹ $\dfrac{3}{4}$

Gain = 50%

Let C.P. = $₹x$.

$\text{Profit \%} = \dfrac{\text{Profit}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$\Rightarrow 50 = \dfrac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{50 \times x}{100}\\[1em] = \dfrac{x}{2}$

As we know:

$\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \dfrac{x}{2} = \dfrac{3}{4} - x\\[1em] \Rightarrow \dfrac{3}{4} = \dfrac{x}{2} + x\\[1em] \Rightarrow \dfrac{3}{4} = \dfrac{x}{2} + \dfrac{2x}{2}\\[1em] \Rightarrow \dfrac{3}{4} = \dfrac{(x + 2x)}{2} \\[1em] \Rightarrow \dfrac{3}{4} = \dfrac{3x}{2}\\[1em] \Rightarrow x = \dfrac{3 \times 2}{4 \times 3}\\[1em] \Rightarrow x = \dfrac{6}{12}\\[1em] \Rightarrow x = \dfrac{1}{2}$

C.P. of 1 orange = ₹ $\dfrac{1}{2}$

C.P. of 4 oranges = ₹ $4\times\dfrac{1}{2}$

= ₹ $\dfrac{4}{2}$

= ₹ 2

Hence, C.P. of 4 oranges = ₹ 2.

(ii) C.P. of 1 orange = ₹ $\dfrac{1}{2}$ = ₹ 0.5

(iii) S.P. of 1 orange = ₹ $\dfrac{3}{4}$ = ₹ 0.75

(iv) Profit = S.P. - C.P.

= ₹ 0.75 - ₹ 0.50

= ₹ 0.25

Hence, Profit = ₹ 0.25.

(v) Gain on 1 orange = ₹ 0.25

Let number of oranges needed to gain ₹ 24 be $x$

Gain on $x$ orange = ₹ 0.25 x $x$ = ₹ 24

⇒ $x = \dfrac{24}{0.25}$

⇒ $x = \dfrac{2400}{25}$

⇒ $x = 96$

Hence, 96 oranges need to be bought and sold in order to gain ₹ 24.