Question

a grocer bought sugar worth of rupees 4500. he sold one third of it at a gain of 10%. at what gain percent must the remaining sugar be sold to have a gain of 12% on the whole?

Answer 1

Given: CP = 4500

Profit on 1/3 of theof the sugar = 10%

Amount = (4500/3)*(110/100)

= 150*11 = 1650

Profit = 1650 - 1500 = 150

Total amount required = 4500*112/100 = 5040

Total profit should be 5040 - 4500 = 540

Required profit on the remaining part of the sugar = 540 - 150 = 390

Let the profit on the remaining part of sugar be x

amount by selling 2/3 of the sugar = (4500)*(2/3)*(x/100) = 390

= 30x = 390

= x = 390/30 = 13

Therefore, profit on the remaining part of the sugar = 13%

Answer 2

Let the sugar be x.....

CP of x = 4500 Rs.
SP needed = CP + 12% Gain
$= 4500 + \frac{12}{100} \times 4500 \\ = 4500 + 540 \\ = 5040$
So, 1/3rd of the Sugar will be x/3.
He sold it at a gain of 10%....
So, SP of x/3 = CP of x/3 + 10% Gain of x/3
$= \frac{4500}{3} + \frac{10}{100} \times \frac{4500}{3} \\ = 1500 + 150 \\ = 1650$
So, Remaining Sugar
$= x - \frac{x}{3} \\ = \frac{3x -x}{3} \\ = \frac{2x}{3}$
And, Remaining SP needed
= 5040 - 1650
= 3390 Rs.
NOW, CP of Remaining Sugar
$\frac{2}{3} \times 4500 \\ = 2 \times 1500 \\ = 3000$
But, SP needed on Remaining Sugar
= 3390 Rs.
So, In order to get 12% gain on the whole transaction he must sell the remaining sugar on =
$\frac{sp}{cp} \times 100 \\ = \frac{3390}{3000} \times 100 \\ = 113\%$