Question

1. In a mixture of 60 litres, the ratio of milk and water is
2:3. How much water must be added to this mixture
so that the ratio of milk and water becomes 1:2?
(a) 10 litres
(b) 12 litres
(c) 15 litres
(d) 20 litres​

Answer 1

$\pmb{ \sf Given : - }$

• In a mixture of 60 litres, the ratio of milk and water is 2:3.

$\pmb{ \sf \: To \: Find : - }$

• Water must be added to this mixture so that the ratio of milk and water becomes 1:2.

$\pmb{ \sf \: Solution:-}$

$\begin{gathered} \sf \: Given \: ratio = 2 : 3 \\ \\ \leadsto \: \sf Sum \: of \: ratios = 2 + 3 \\ \leadsto \sf \: \purple 5\end{gathered}$

$\begin{gathered} \sf \: Quantity \: of \: milk = \frac{2}{ \cancel5} \times \cancel{ 60} \\ \leadsto \sf \: 2 \times 12 \\ \leadsto \bf \purple{24 \: l}\end{gathered}$

$\begin{gathered} \sf \: Quantity \: of \: water = 60 - 24 \\ \dashrightarrow \bf \purple{36 \: l}\end{gathered}$

Now,

$\bigstar \rm \: \: Let \pink{ \bf \: x l} \: be \: added$

ACQ,

$\begin{gathered} \therefore \tt \: \frac{24}{36 + x} = \frac{1}{2} \\ \longrightarrow \tt \: 1(36 + x) = 2(24) \\ \longrightarrow \tt \: 36 + x = 48 \\ \longrightarrow \tt \: x = 48 - 36 \\ \longrightarrow \tt \: \bf \color{aqua} \: x = 12 \: l\end{gathered}$

So,

The amout added = 12 l

[Option 'B' supports the answer]