3 litres of liquid M is taken and mixed with 5 litres of liquid N. The mixture is divided into four equal parts. In one of these parts, some amount of liquid M is added so that the ratio of M and N in this part becomes 6:5. Now, all parts are mixed back together. What will be the ratio of liquids M and N in the total mixture now?
Solution
Correct Answer: Option B
3 liters of liquid M and 5 liters of liquid N are mixed.
Total volume of mixture = (3+5) liters = 8 liters
After dividing into 4 equal parts,
Volume of each part = (8/4) liters = 2 liters
Volume of liquid M in each part = (3÷ (3+5)) ×2 = 0.75 liters.
Volume of liquid N in each part = (5÷ (3+5)) ×2 = 1.25 liters.
Suppose T liters of liquid M are added in one of these parts to make ratio of M and N to 6:5 in this part.
⇒ (0.75 + T)/1.25 = 6/5
⇒ 3.75 + 5T = 7.5
⇒ 5T = 3.75
⇒ T = 0.75
Now, all parts are mixed back together.
Volume of liquid M in mixture = (3 + 0.75) liters = 3.75 liters.
Volume of liquid N in mixture = 5 liters.
∴ Ratio of liquids M and N = 3.75: 5 = 3:4
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