Question

A salesman deals in paint and 65 litre mixture is to be distributed in paint & Water
in the ratio of 4: 1. If 8 litre paint & 7 litre water will be added in the mixture then
what will be the new ratio of water and paint?​

Answer 1

★ How to do :-

Here, we are given with the total amount of the mixture of paint and water. We are also given with the ratio that is added to the mixture. We are asked to find the new ratio of the paint and water if the eight litre of paint and seven litre of water is still added to the mixture. So, first we should find the total amount of water and mixture that was there before adding the extra mixture in it. Then, we can add the extra amount of litres added to each of them separately and then, we can find the ratio between them. To find the answer we use an other concept called as the variables. This is to be used when we are finding the values of the water and paint with the help of the ratio and the total litres of the mixture. So, let's solve!!

$\:$

➤ Solution :-

${\sf \leadsto 4 : 1 = 65}$

Insert a variable x to both parts of ratio.

${\sf \leadsto 4x + 1x = 65}$

Add both values on the LHS.

${\sf \leadsto 5x = 65}$

Shift the number 5 from LHS to RHS.

${\sf \leadsto x = \dfrac{65}{5}}$

Simplify the fraction to get the value of x.

${\sf \leadsto x = 13}$

$\:$

Now, multiply the value of x with both parts of ratios.

Litres of paint :-

${\sf \leadsto 4x = 4 \times 13}$

Multiply the values to get the amount of paint.

${\sf \leadsto 52 \: \: litres}$

Litres of water :-

${\sf \leadsto 1x = 1 \times 13}$

Multiply the values to get the litres of water.

${\sf \leadsto 13 \: \: litres}$

$\:$

Now, let's add the extra paint and water to the present mixture.

New amount of paint :-

${\sf \leadsto 52 + 8}$

Add the values to get the total amount of paint.

${\sf \leadsto 60 \: \: litres}$

New amount of water :-

${\sf \leadsto 13 + 7}$

Add the values to get the total amount of paint.

${\sf \leadsto 20 \: \: litres}$

$\:$

Now, let's find the new ratio of the paint and water.

${\sf \leadsto 60 : 20 = \dfrac{60}{20}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{60}{20}}$

${\sf \leadsto \dfrac{1}{3} = 1 : 3}$

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${\red{\underline{\boxed{\bf So, \: the \: new \: ratio \: is \: 1:3.}}}}$