A shopkeeper bought rice worth ₹ 4,500. He sold one-third of it at 10% profit. If he desires a profit of 12% on the whole, find :

(i) the selling price of the rest of the rice.

(ii) the percentage profit on the rest of the rice.

(i) Given:

C.P. of whole rice = ₹ 4,500

Profit desired on the whole = 12 %

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

Putting the values, we get

$12 = \dfrac{\text{Profit}}{4,500} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{12 \times 4,500}{100}\\[1em] = \dfrac{54,000}{100}\\[1em] = 540$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$540 = \text{S.P.} - 4,500\\[1em] \Rightarrow \text{S.P.} = 540 + 4,500\\[1em] = 5,040$

C.P. of $\dfrac{1}{3}$rice = ₹ $\dfrac{1}{3} \times 4,500$

= ₹ $\dfrac{4,500}{3}$

= ₹ $1,500$

Gain on it = 10%

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

Putting the values, we get

$10 = \dfrac{\text{Profit}}{1,500} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{10 \times 1,500}{100}\\[1em] = \dfrac{15,000}{100}\\[1em] = 150$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$150 = \text{S.P.} - 1,500\\[1em] \Rightarrow \text{S.P.} = 150 + 1,500\\[1em] = 1,650$

The S.P. of the rest of the rice = ₹ 5,040 - ₹ 1,650 = ₹ 3,390

The selling price of the rest of the rice = ₹ 3,390.

(ii) C.P. of the rest of the rice = ₹ 4,500 - ₹ 1,500 = ₹ 3,000

Profit on the rest of the rice = Remaining S.P. - Remaining C.P.

= ₹ 3,390 - ₹ 3,000

= ₹ 390

$\text{Profit\%} = \dfrac{Profit}{C.P.}\times 100\%\\[1em] = \dfrac{390}{3000}\times 100\%\\[1em] = \dfrac{13}{100}\times 100\%\\[1em] = \dfrac{1300}{100}\%\\[1em] = 13$

The profit percentage of rest of the rice = 13%.