IPMAT Indore 2022 · Quantitative Ability · Question 30

IPMAT Indore 2022 previous year question on Mixtures and Alligation, with the answer and a step-by-step solution.

Mixtures and AlligationArithmeticMultiple choiceMedium
In a bowl containing 60 ml orange juice, 40 ml of water is poured. Thereafter, 100 ml of apple juice is poured to make a fruit punch. Madhu drinks 50 ml of this fruit punch and comments that the proportion of orange juice needs to be higher for better taste. How much orange juice should be poured into the fruit punch that remained, in order to bring up the level of orange juice to 50 percentage?
  1. A
    100 ml
  2. B
    40 ml
  3. C
    80 ml
  4. D
    60 ml
Pick an option, then check.
Answer & solution

Answer: Option D

Step 1 — compose the punch.

60\text{(orange)}+40\text{(water)}+100\text{(apple)}=200\text{ml}

The orange fraction is \frac{60}{200}=30\%.

Step 2 — remove 50 ml. Madhu drinks a well-mixed 50 ml, i.e. one quarter of the punch. Every component is reduced by a quarter, leaving three quarters of each:

\text{orange}=3/4\left( 60 \right)=45\text{ml}, \text{total}=150\text{ml}

Step 3 — add x ml of orange juice and require 50%. After adding, the orange is 45+x and the total is 150+x:

\frac{45+x}{150+x}=\frac{1}{2}

Step 4 — solve.

2\left( 45+x \right)=150+x \Rightarrow 90+2x=150+x \Rightarrow x=60

Check: orange =105, total =210, and \frac{105}{210}=50\% ✔

Answer: Option 4 — 60 ml

Shortcut. Track the non-orange part — it never changes once drinking stops. After Madhu drinks a quarter, the non-orange liquid is 3/4\left( 140 \right)=105 ml, and adding orange juice leaves it untouched.

For the mixture to be 50% orange, the orange must simply equal the non-orange:

\text{orange needed}=105, \text{already present}=45 \Rightarrow x=60

This “hold the other component fixed” trick turns every “raise the concentration to 50%” question into a subtraction. For a target of 1/3 or 1/4 instead, scale the fixed part accordingly — it is still one line.

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