A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 liters of milk such that the ratio of water to milk is 3 : 5?

Created: 3 months ago | Updated: 3 months ago

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প্রশ্নে বলা হচ্ছে, একজন গোয়ালার দুটি দুধের পাত্র আছে। প্রথম পাত্রে 25% পানি ও বাকি দুধ আছে। দ্বিতীয় পাত্র 50% পানি ধারণ করছে। প্রত্যেক পাত্র হতে কি পরিমাণ দুধ মেশালে 3 : 5 অনুপাতের মিশ্রণে 12 লিটার দুধ পাওয়া যাবে?

Let, each cans 'x' and 'y' litters of milk and water should be mixed to get water to milk 3 : 5

Can-1: Water = x of 25% $x \times \frac{25}{100} = \frac{x}{4}$

Milk = x of (100-25)% = x of 75% $= \frac{3 x}{4}$

Can-2: Water = y of 50% $= \frac{y}{2}$

Milk = y of (100 – 50)% = y of 50% $= \frac{y}{2}$

According to the question

$(\frac{x}{4} + \frac{y}{2}) : (\frac{3 x}{4} + \frac{y}{2}) = 3 : 5$

$\Rightarrow \frac{\frac{x}{4} + \frac{y}{2}}{\frac{3 x}{4} + \frac{y}{1}} = \frac{3}{5}$

$\Rightarrow \frac{\frac{x + 2 y}{4}}{\frac{3 x + 2 y}{4}} = \frac{3}{5}$

$\Rightarrow \frac{x + 2 y}{3 x + 2 y} = \frac{3}{5}$

$\Rightarrow 5 (x + 2 y) = 3 (3 x + 2 y)$

$\Rightarrow 5 x + 10 y = 9 x + 6 y$

$\Rightarrow 10 y - 6 y = 9 x - 5 x$

$\Rightarrow 4 y = 4 x$

$∴ x : x = 1 : 1$

Sum of ratio = 1+1=2

∴ Each can milk should be mixed $= 12 \times \frac{1}{2} = 6 l i t e r s$

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A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 liters of milk such that the ratio of water to milk is 3 : 5?

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