Question

A mixture of rice and wheat contains 70% wheat.what percentage of the mixture should be removed and substituted with rice such that the resultant mixture contains wheat and rice in the ratio 14:11?​

Answer 1

Answer: 30%should be removed

Step-by-step explanation:

Answer 2

The percentage of the mixture should be removed is 20 %.

Step-by-step explanation:

Given:

A mixture of rice and wheat contains 70% wheat.

Removed  mixture will be substituted with rice.

The ratio of  wheat and rice in resultant mixture  is 14:11

To Find:

The percentage of the mixture should be removed .

Formula Used:

The ratio of  two quantities m and n  is defined as;

$m:n=\frac{m}{n}$

Solution:

As given - A mixture of rice and wheat contains 70% wheat   .

Let the amount of rice in original mixture is 3p.

Let the amount of  wheat  in original mixture is 7p.

Let q  amount of  mixture  was removed.

The remaining amount of rice  in mixture  $=3p-q\times\frac{3}{10}$

                                                                     $=3p-\frac{3q}{10}$     ------ equation no. 01

The remaining amount of  wheat   in mixture $=7p-q\times\frac{7}{10}$  

                                                                   $=7p-\frac{7q}{10}$  ---------  equation no.02

As given - Removed  mixture will be substituted with rice.

So, the  amount of rice  in  resultant  mixture  $=3p-\frac{3q}{10}+q$

                                                                     $=3p+\frac{7q}{10}$           - equation no.03

As given - The ratio of  wheat and rice in resultant mixture  is 14:11

From equation no.02 and equation no. 03.    

  $\frac{7p-\frac{7q}{10}}{3p+\frac{7q}{10}} =\frac{14}{11}$

$11(7p-\frac{7q}{10}) = 14(3p+\frac{7q}{10})$

$77p-\frac{77q}{10} =42 p+\frac{98q}{10}$

$35p = \frac{175q}{10}$

$p=\frac{5q}{10}$

$p=\frac{q}{2}$

$q=2p$

Now original  weight of  mixture $= 3p+7p$

        Original  weight of  mixture $=10p$

     Amount of mixture removed $q=2p$

Therefore,% of mixture removed  will be 20%.

Thus, The percentage of the mixture should be removed  20%.