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Two parts at different percentage rates with a known overall rate: find the split (alligation)

This type of question, asked 4 times: 17 Jul 2023 S2, 20 Jul 2023 S1, 24 Sep 2024 S2, 21 Sep 2025 S2. All 4 questions below, oldest first.

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  1. Question 1

    17 Jul 2023 S2

    69
    Suhani pays tax at the rate of 30% on her entire income of ₹90,000 and Ritika pays tax at the rate of 40% on her entire income of ₹y. If the overall tax rate on their combined income comes to 37%, then what is the value of y?

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  2. Question 2

    20 Jul 2023 S1

    52
    In a certain year, the population of a city was 18000. If in the next year, the population of males increased by 5%5\% and that of females increased by 7%7\%, and the total population increased to 19200, then what was the ratio of the populations of males and females in that given year?

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  3. Question 3

    24 Sep 2024 S2

    73
    A person purchased a table and a sofa for ₹28,000. He sold the sofa at a profit of 10% and the table at a profit 15.25%. If his total profit was 13%, then the difference between the cost price of the sofa and the table (in ₹) is:

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  4. Question 4

    21 Sep 2025 S2

    61
    A person invested in two items — one gave a 10%10\% profit and the other a 5%5\% loss. If the total investment was Rs. 5,000 and the net result was a Rs. 100 profit, what was the investment in the profit-making item?

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