Question
Download Solution PDFA drink is made by mixing water and juice in the ratio 9 ∶ 7. If x litres of water and 2x litres of juice are mixed in 160 litres of drink, then the new ratio becomes 13 ∶ 15. The quantity of drink (in litres) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A drink is made by mixing water and juice in the ratio 9 ∶ 7.
If x litres of water and 2x litres of juice are mixed in 160 litres of drink, then the new ratio becomes 13 ∶ 15.
Formula used:
Initial ratio of water to juice = 9/7
New ratio of water to juice = 13/15
Calculation:
Given initial ratio: 9/7
New ratio: 13/15
Total drink = 160 litres
Let x be the litres of water and 2x be the litres of juice added.
Total water = (9/16) × 160 + x = 90 + x
Total juice = (7/16) × 160 + 2x = 70 + 2x
New ratio: (90 + x)/(70 + 2x) = 13/15
⇒ 15(90 + x) = 13(70 + 2x)
⇒ 1350 + 15x = 910 + 26x
⇒ 1350 - 910 = 26x - 15x
⇒ 440 = 11x
⇒ x = 40
Total quantity of drink = 160 + x + 2x
⇒ Total quantity = 160 + 40 + 80
⇒ Total quantity = 280 litres
∴ The correct answer is option 2.
Last updated on May 28, 2025
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