Averages , Ratio and Proportion Question 2 - CAT 2020
A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is 3 : 2, while the ratio of the shares of Sunil and Mita is 4 : 5. If the difference between the largest and the smallest of these three shares is Rs. 400, then Sunil’s share, in rupees, is:
Step-by-Step Explanation
- Combine the individual ratios:
We are given two separate ratios:
Amal : Sunil = 3 : 2
Sunil : Mita = 4 : 5
To combine these into a single joint ratio, we synchronize the value of Sunil's share, which acts as the bridge between both ratios. Multiply the Amal : Sunil ratio by 2:
Amal : Sunil = 6 : 4
Now, combine the expressions cleanly:
Amal : Sunil : Mita = 6 : 4 : 5
- Apply the difference constraint:
Let the shares be 6k, 4k, and 5k respectively.
Largest share = 6k (Amal)
Smallest share = 4k (Sunil)
The difference between the largest and smallest shares is given as Rs. 400:
6k − 4k = 2k = 400
k = 200
- Calculate Sunil's absolute share:
Sunil's Share = 4k
= 4 × 200
= Rs. 800
Correct Answer: 800
💡 FundaMakers Tip:
When working with multiple ratio structures, always check if the question can be solved using parts conversion directly. Once the joint ratio 6 : 4 : 5 is established, you can see that the gap between the extremes is exactly 2 parts (6 − 4). Mapping these 2 parts directly to the absolute value of Rs. 400 shows that each individual ratio part is worth exactly Rs. 200. Sunil's share is 4 parts, which gives 4 × 200 = 800 immediately without writing out algebraic equations.