Question

a farmer mixes two varities of rice of price Rs.72 per kg and Rs. 48 per kg in the ratio of 1:2. he sold the mixture for Rs.4200 to earn a profit of 25%. find the quantity of rice of cost Rs.72 per kg in the mixture.​

Answer 1

72+ 48*2 72+96=168
Cp =4200*100/125 4200*4/5= 16800/5=3360
1/168*3360=20 kg

Answer 2

The quantity of rice of cost Rs.72 per kg in the mixture is 20 kg and option A is correct.

Step-by-step explanation:

Given:

A farmer mixes two varieties of rice of price Rs.72 per kg and Rs. 48 per kg in the ratio of 1:2.

Farmer sold the mixture for Rs.4200 to earn a profit of 25%.

To Find:

The quantity of rice of cost Rs.72 per kg in the mixture.

Formula Used:-

$\frac{ Quantity\ of\ Cheaper\ rice}{Quantity\ of\ Dearer\ rice} =\frac{Cost\ Price\ of\ Dearer\ rice- Mixtrure\ rice\ Price}{Mixture\ rice\ Price- Cost\ Price\ of\ Cheaper\ rice]}$

he above as per  rule of of allegation.

Solution:

As given-a farmer mixes two varieties of rice of price Rs.72 per kg and Rs. 48 per kg in the ratio of 1:2.

Cost of 1 kg dearer  rice cost Rs. 72.

Cost of 1 kg cheaper rice cost Rs.48.

Let cost of 1 kg   rice  mixture cost  is  Rs. p.

$\frac{ Quantity\ of\ dearer\ rice}{Quantity\ of\ cheaper\ rice} =\frac{1}{2}$

Applying formula no. 01. we get.

$\frac{ Quantity\ of\ Cheaper\ rice}{Quantity\ of\ Dearer\ rice} =\frac{72-p}{p-48}$

$\frac{2}{1} =\frac{72-p}{p-48}$

$2p-96=72-p$

$3p= 168$

$p= Rs.56$

As given- farmer sold the mixture for Rs.4200 to earn a profit of 25%.

$Selling\ price\ of\ mixture = Cost\ price\ of\ mixture (1+\frac{profit}{100} )$

$4200 = Cost\ price\ of\ mixture (1+\frac{25}{100} )$

$4200= 1.25 \times Cost\ price\ of\ mixture$

$Cost\ price\ of\ mixture =\frac{4200}{1.25} = Rs. 3360$

Therefore, total quantity of mixture of rice $=\frac{3360}{56} =60kg$

So, required quantity of rice of cost Rs.72 per kg in the mixture

=  $\frac{1}{3} \times 60= 20 kg$                                                  

Thus, required quantity of rice of cost Rs.72 per kg in the mixture is 20 kg  and option A is correct.

PROJECT CODE#SPJ2