Question

A grocer bought one quintal of rice at Rs.24kg. He sold 75kg of it at the rate of Rs 26 per kg. At what rate per kg must he sell the remainder to gain 15% on the whole?

Answer 1

Hint: Assume that the rate at which the remainder is sold be Rs. x/kg. Calculate the gain% age using $gain%=\dfrac{gain}{C.P}\times 100$ in terms of x. Equate this expression to 15% as there is a net 15% gain on the whole. Hence form a linear equation in x. Solve for x. The value of x will give the rate at which the remainder must be sold so that the grocer gains 15% on the whole.

Important conversion: 1 Quintal = 100kg

Complete step-by-step answer:

We have cost price of 1 kg of rice = Rs 24

Hence the cost price of 1 Quintal of rice $=24\times 100=\text{Rs}\text{. 2400}$

So, the grocer bought 1 quintal of rice for Rs. $2400$

The grocer sold 75 kg of rice at  Rs 26/kg

Amount earned by selling 1 kg of rice = Rs. $26$

Hence amount earned by selling 75kg of rice = $26\times 75$= Rs. $1950$

So the remaining amount of rice to be sold = $100$kg-$75$kg =$25$kg

Let the grocer sell the remaining amount at Rs$x$/kg so that he gains $15$% on the whole.

Amount earned by selling 1 kg of remaining amount = Rs$x$.

Hence the amount earned by selling 25 kg of the remaining amount = Rs.$25x$

Hence the total selling price = $1950+25x$

Profit earned = Selling price - Cost price = $1950+25x-2400$ = Rs.$25x-450$

Hence profit %age = $\dfrac{\text{Profit}}{\text{C}\text{.P}}\times 100$=$\dfrac{25x-450}{2400}\times 100$

But according to the question we have gain %age = $15$.

Equating we get

$\dfrac{25x-450}{2400}\times 100=15$

Multiplying both sides of the equation by 2400 we get

$\Rightarrow \dfrac{25x-450}{2400}\times 2400\times 100=15\times 2400$

$\Rightarrow (25x-450)\times 100=15\times 2400$

Dividing both sides of the equation by 100 we get

$\Rightarrow 25x-450=\dfrac{15\times 2400}{100}$

$\Rightarrow 25x-450=360$

Adding 450 to both sides of equation

$\Rightarrow 25x-450+450=360+450$

$\Rightarrow 25x=810$

Dividing both sides of equation by 25 we get

$\Rightarrow \dfrac{25x}{25}=\dfrac{810}{25}$

$\Rightarrow x=32.4$

Hence the grocer should sell the amount at $32.4$/kg to get a gain of $15\%$.

Note: Sometimes instead of giving rate per unit the rate may be given per some number of units.Ex. The rate at which the rice is sold can be given as Rs15 per 3 kg of rice.

In this case we use a unitary method i.e. find the rate per kg and then follow the above procedure.

Selling 3 kg of rice earns Rs.15

Hence selling of 1 kg of rice earns $\dfrac{15}{3}$= Rs $5$

Now if we want to find how much we can earn by selling 75 kg we can do it the same way as done in above question

i.e. Selling 75 kg of rice earns $75\times 5$= Rs 375

This is known as the unitary method.