Question

A grocer bought sugar worth rs 4500. He sold third of it at a gain of 10 %.At what gain per cent must the remaining sugar be sold to have a gain of 12 % on the whole.

Answer 1

answer is 13%...
I hope you will like my explanation.

Answer 2

Answer:

Gain percent of the remaining sugar is 13%.

Step-by-step explanation:

Given : A grocer bought sugar worth rs 4500. He sold third of it at a gain of 10 %.

To find : At what gain per cent must the remaining sugar be sold to have a gain of 12 % on the whole?

Solution :

The cost price of the sugar is Rs.4500.

He sold third of it at a gain of 10 %.

The cost price of one-third of sugar is $\frac{1}{3}\times 4500=1500$

The selling price is $SP=CP[\frac{100+P\%}{100}]$

$SP=1500[\frac{100+10}{100}]$

$SP=1500[\frac{110}{100}]$

$SP=1650$

The selling price of one-third of the sugar is Rs.1650.

Profit = SP-CP

Profit = 1650-1500

Profit =Rs.150

Gain of 12% on the whole.

The selling price of the whole is $SP=CP[\frac{100+P\%}{100}]$

$SP=4500[\frac{100+12}{100}]$

$SP=4500[\frac{112}{100}]$

$SP=5040$

The selling price of the whole is Rs.5040.

Profit = SP-CP

Profit = 5040-4500

Profit = Rs.540

Profit of remaining sugar = 540 - 150 = 390.

Cost price of remaining sugar = (4500 - 1500) = 3000.

Gain percentage is given by,

$G\%=\frac{P}{CP}\times 100$

$G\%=\frac{390}{3000}\times 100$

$G\%=13\%$

Therefore, Gain percent of the remaining sugar is 13%.