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A 40-liter mixture contains juice and water in the ratio 5:3. How much water (in liters) must be added to this mixture to change the ratio of juice to water to 2:3?

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A 40-liter mixture contains juice and water in the ratio 5:3. How much water (in liters) must be added to this mixture to change the ratio of juice to water to 2:3?

40 लीटर के मिश्रण में जूस और पानी का अनुपात 5:3 है। जूस और पानी का अनुपात 2:3 करने के लिए इसमें कितना पानी (लीटर में) मिलाना होगा?

Options / विकल्प

A. 15.5 litres

B. 22.5 litres ✅

C. 25 litres

D. 30 litres

Answer / उत्तर

✅ 22.5 litres

Solution / समाधान

Method 1: Direct Calculation

विधि 1: प्रत्यक्ष गणना

Initial ratio:

Juice : Water=5:3\text{Juice : Water} = 5 : 3

Total mixture:

40 litres40 \text{ litres}

Juice:

58×40=25 litres\frac{5}{8}\times 40 = 25 \text{ litres}

Water:

38×40=15 litres\frac{3}{8}\times 40 = 15 \text{ litres}

Let xx litres of water be added.

Then,

2515+x=23\frac{25}{15+x}=\frac{2}{3}

Cross-multiplying:

75=30+2x75=30+2x
2x=452x=45
x=22.5x=22.5

Shortcut Trick / शॉर्टकट ट्रिक

Since only water is added, the quantity of juice remains constant.

केवल पानी मिलाया गया है, इसलिए जूस की मात्रा स्थिर रहेगी।

Make juice units equal:

5:3×2=10:65:3 \times 2 = 10:6
2:3×5=10:152:3 \times 5 = 10:15

Initial mixture:

10+6=16 units=40 litres10+6=16 \text{ units} = 40 \text{ litres}
1 unit=4016=2.5 litres1 \text{ unit} = \frac{40}{16}=2.5 \text{ litres}

Extra water required:

15−6=9 units15-6=9 \text{ units}
9×2.5=22.5 litres9\times 2.5 = 22.5 \text{ litres}

Final Answer / अंतिम उत्तर

22.5 litres\boxed{22.5 \text{ litres}}

✅ Correct Answer / सही उत्तर: 22.5 litres / 22.5 लीटर


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