Question

The ratio of the milk and water in 85 litres of milk is 27:7. Find the amount of water that must be added to make the ratio 3:1.​

Answer 1

AnswEr :

5 litres.

$\bf{\green{\underline{\underline{\bf{Given\::}}}}}$

The ratio of the milk and water in 85 litres of milk is 27:7. And must be added to make the ratio 3:1.

$\bf{\green{\underline{\underline{\bf{To\:find\::}}}}}$

The amount of water.

$\bf{\green{\underline{\underline{\bf{Explanation\::}}}}}$

Let the amount of milk be r litres.

Let the amount of water be (85-r) litres

A/q

$\bf{\large{\underline{\underline{\bf{1_{st}\:Case\::}}}}}$

$\mapsto\sf{m:(85-m)=27:7}\\\\\\\mapsto\sf{\dfrac{r}{85-r} =\dfrac{27}{7} }\\\\\\\mapsto\sf{7(r)=27(85-r)}\\\\\\\mapsto\sf{7r=2295-27r}\\\\\\\mapsto\sf{7r+27r=2295}\\\\\\\mapsto\sf{34r=2295}\\\\\\\mapsto\sf{r=\cancel{\dfrac{2295}{34} }}\\\\\\\mapsto\sf{\red{r=67.5}}$

So, we have milk = 67.5 litres.

&

$\leadsto\sf{Water\:mixed=(85-67.5)\:litres}\\\\\leadsto\sf{\red{Water\:mixed=17.5\:litres}}$

$\bf{\large{\underline{\underline{\bf{2_{nd}\:Case\::}}}}}$

Let the amount of water added be x litres

A/q

$\leadsto\sf{3:1=67.5:(17.5+x)}\\\\\\\leadsto\sf{\dfrac{3}{1} =\dfrac{67.5}{17.5+x} }\\\\\\\leadsto\sf{3(17.5+x)=67.5}\\\\\ \\\leadsto\sf{52.5+3x=67.5}\\\\\\\leadsto\sf{3x=67.5-52.5}\\\\\\\leadsto\sf{3x=15}\\\\\\\leadsto\sf{x=\cancel{\dfrac{15}{3} }}}\\\\\\\leadsto\sf{\red{x=5\:litres}}$

Thus;

The amount  of water must be added = 5 litres.

Answer 2

AnswEr:-

5 litres of water must added.

$\rule{200}{1}$

Given:-

• Total amount = 85 l
• Ratio of milk & water = 27 : 7
• New ratio = 3 : 1

To find:-

• Amount of water should be added.

Solution:-

Let amount of milk & water be 27y & 7y.

According to question:-

⇒ 27y + 7y = 85

⇒ 34y = 85

⇒ y = 85/34

⇒ y = 2.5 l

⋆ AMOUNT OF WATER & MILK:-

↠Amount of milk = 27y = 27(2.5) = 67.5 l

↠Amount of water = 7y = 7(2.5) = 17.5 l

$\rule{200}{1}$

New ratio = 3 : 1

Let the new amount that should be added be y l

According to question:-

⇒ (67.5) : (17.5 + y) = 3 : 1

⇒ (67.5)/(17.5 + y) = 3

⇒ 3(17.5 + y) = 67.5

⇒ 52.5 + 3y = 67.5

⇒ 3y = 67.5 - 52.5

⇒ 3y = 15

⇒ y = 15/3

⇒ y = 5 litres.

$\therefore\underline{\textsf{Water must be added = {\textbf{5 litres }}}}$