A mango juice is made by mixing water and mango concentrate in the ratio 9 : 7. If x litres of water and 3x litres of mango concentrate is mixed in 160 litres of mango juice, then the new ratio becomes 13 : 14. What is the quantity of the new mango juice (in litres)?

Question

Accepted Answer

Step 1: Initial ratio of water to mango concentrate = 9 : 7
Step 2: Total initial juice = 160 litres
Step 3: Amount of water initially = (9/16) * 160 = 90 litres
Step 4: Amount of mango concentrate initially = (7/16) * 160 = 70 litres
Step 5: Additional water added = x litres
Step 6: Additional mango concentrate added = 3x litres
Step 7: New water quantity = 90 + x
Step 8: New mango concentrate quantity = 70 + 3x
Step 9: New ratio given = 13 : 14
Step 10: Set up equation:
(90 + x) / (70 + 3x) = 13 / 14
Cross multiply:
14(90 + x) = 13(70 + 3x)
1260 + 14x = 910 + 39x
1260 - 910 = 39x - 14x
350 = 25x
x = 350 / 25 = 14 litres
Step 11: New total quantity = initial 160 + added water and concentrate = 160 + x + 3x = 160 + 4x = 160 + 4*14 = 160 + 56 = 216 litres
Step 12: Verify ratio:
Water = 90 + 14 = 104 litres
Mango concentrate = 70 + 42 = 112 litres
Ratio = 104 : 112 = 13 : 14 (correct)
Step 13: The new quantity of mango juice is 216 litres.

Note: The answer options given are 197, 212, 206, 216. The correct answer is 216 litres.

Answer

Answer

Answer