11. Practice Question Set B — Moderate / Exam Level (30 MCQs)

This set mirrors the phrasing and difficulty of actual SSC CGL/CHSL Tier-1 and RRB NTPC/Group D questions — chained ratios across four terms, compound partnership with mid-year capital changes, simultaneous income-expenditure-savings ratios, reverse componendo-dividendo, and ratio combined with percentage in group-split contexts. These questions typically take 45–75 seconds each once the shortcut techniques are internalised; without them, they can easily consume 2 minutes or more.

B1. [Ratio + LCM] The ratio of two numbers is 3 : 4, and their LCM is 180. Find the sum of the numbers. (a) 105 (b) 100 (c) 115 (d) 90

B2. [Dividing a Sum, Chained Ratio] A sum of ₹6300 is divided among A, B, C such that A : B = 2 : 3 and B : C = 4 : 5. Find C’s share. (a) ₹2700 (b) ₹2400 (c) ₹2100 (d) ₹3000

B3. [Compound Partnership with Mid-Year Change] A and B start a business investing ₹35,000 and ₹45,000 respectively. After 4 months, A withdraws ₹5,000 and B invests ₹5,000 more. Find the profit-sharing ratio at the end of the year. (a) 19 : 29 (b) 7 : 9 (c) 35 : 45 (d) 2 : 3

B4. [Income–Expenditure Simultaneous Ratios] The incomes of A and B are in the ratio 3 : 2, and their expenditures are in the ratio 5 : 3. If each saves ₹1000, find A’s income. (a) ₹6000 (b) ₹4000 (c) ₹5000 (d) ₹3000

B5. [Reverse Componendo-Dividendo] If (x+y) : (x−y) = 3 : 2, find x : y. (a) 5 : 1 (b) 3 : 2 (c) 1 : 5 (d) 2 : 3

B6. [Compound Partnership, Fractional Ratio + Mid-year Increase] A, B, C enter a partnership investing in the ratio 1/2 : 1/3 : 1/4. After 4 months, A increases his investment by 50%. If the total profit at year-end is ₹21,600, find B’s share. (a) ₹5760 (b) ₹6000 (c) ₹5400 (d) ₹4800

B7. [Age Ratio, Past & Present] The ratio of ages of P and Q, 6 years ago, was 3 : 4. If the ratio of their present ages is 4 : 5, find Q’s present age. (a) 30 (b) 24 (c) 32 (d) 28

B8. [Ratio + Percentage, Group Split] In a school, the ratio of boys to girls is 5 : 4. If 40% of the boys and 25% of the girls receive a scholarship, what percentage of the total students receive a scholarship? (a) 33.33% (b) 30% (c) 36% (d) 40%

B9. [Ratio with Constant Subtracted] Two numbers are in the ratio 5 : 6. If 8 is subtracted from each, the ratio becomes 4 : 5. Find the numbers. (a) 40, 48 (b) 35, 42 (c) 45, 54 (d) 30, 36

B10. [Inverse Proportion / Efficiency] A alone can complete a work in 12 days and B alone in 18 days. Find the ratio of their efficiencies. (a) 3 : 2 (b) 2 : 3 (c) 1 : 2 (d) 3 : 1

B11. [Chained Ratio, Four Terms] If a : b = 2 : 3, b : c = 5 : 4, c : d = 6 : 7, find a : d. (a) 5 : 7 (b) 3 : 4 (c) 4 : 7 (d) 7 : 5

B12. [Advanced Income-Expenditure-Savings] The ratio of monthly incomes of A and B is 8 : 5, and the ratio of their expenditures is 5 : 3. If A saves ₹2400 per month, which is 25% of his income, find B’s savings. (a) ₹1680 (b) ₹1800 (c) ₹1500 (d) ₹2000

B13. [Dividing a Sum, 4-part with Difference] A sum of money is divided among A, B, C, D in the ratio 3 : 4 : 5 : 6. If D gets ₹600 more than A, find the total sum. (a) ₹3600 (b) ₹3200 (c) ₹4200 (d) ₹3000

B14. [Algebraic Ratio Evaluation] If x/y = 7/3, find the value of (x² − y²)/(x² + y²). (a) 20/29 (b) 29/20 (c) 10/29 (d) 19/29

B15. [Ratio + Mixture Link] A mixture of 45 litres has milk and water in the ratio 4 : 1. How many litres of water must be added so that the ratio becomes 3 : 2? (a) 15 (b) 12 (c) 18 (d) 20

B16. [Continued Ratio, Sum Condition] The ages of A, B and C are in the ratio 2 : 3 : 4. If the sum of the ages of A and C exceeds B’s age by 36 years, find C’s age. (a) 44 years (b) 48 years (c) 40 years (d) 36 years

B17. [Compound Partnership, Two Partners with a Mid-Year Increase and Withdrawal] A and B started a business with capitals of ₹42,000 and ₹56,000 respectively. After 5 months, A increased his capital by ₹8,000 while B withdrew ₹6,000. Find the profit-sharing ratio at the end of the year. (a) 8 : 9 (b) 9 : 8 (c) 4 : 3 (d) 3 : 4

B18. [Mean Proportional, Reverse-solve] The mean proportional between two numbers is 24, and one of the numbers is 18. Find the other number. (a) 28 (b) 36 (c) 32 (d) 30

B19. [Componendo-Dividendo] If (4x + 3y)/(4x − 3y) = 7 : 3, find x : y. (a) 8 : 15 (b) 7 : 3 (c) 3 : 7 (d) 15 : 8

B20. [Income and Expenditure] The ratio of income to expenditure of a man is 7 : 5. If his monthly income is ₹35,000, find his monthly savings. (a) ₹10,000 (b) ₹8,000 (c) ₹12,000 (d) ₹7,000

B21. [Ratio + Successive Percentage Change] Two numbers are in the ratio 3 : 4. The first number is increased by 25% and the second by 50%. Find the new ratio. (a) 3 : 4 (b) 5 : 8 (c) 4 : 5 (d) 8 : 5

B22. [Inverse Proportion / Efficiency + Partial Work] A can do a piece of work in 20 days and B in 30 days. They work together for 4 days, and then A leaves. In how many days will B alone finish the remaining work? (a) 18 (b) 15 (c) 20 (d) 24

B23. [Third and Fourth Proportional Combined] The third proportional to 6 and 12 is x, and the fourth proportional to 3, 4 and 9 is y. Find x − y. (a) 12 (b) 10 (c) 14 (d) 16

B24. [Ratio + Mixture, Reverse Add-on] A mixture of 55 litres contains milk and water in the ratio 7 : 4. How many litres of water must be added to make the ratio 7 : 6? (a) 12 (b) 8 (c) 15 (d) 10

B25. [Continued Ratio, Age Sum] The ratio of the ages of A, B and C is 3 : 5 : 7. If the sum of their ages is 75 years, find B’s age five years hence. (a) 25 (b) 30 (c) 35 (d) 28

B26. [Ratio + Percentage, Attendance Split] The ratio of the number of boys to girls in a class is 7 : 5. If 20% of the boys and 40% of the girls are absent on a particular day, what percentage of the total students are present? (a) 71.67% (b) 70% (c) 75% (d) 66.67%

B27. [Reverse Componendo-Dividendo, Reciprocal Form] If (7a − 2b)/(7a + 2b) = 3/5, find a : b. (a) 7 : 8 (b) 5 : 3 (c) 8 : 7 (d) 3 : 5

B28. [Partnership with Working Partner’s Fee] A and B invest ₹45,000 and ₹55,000 respectively in a business. B manages the business and receives 10% of the total profit as a management fee before the remainder is split in the investment ratio. If the total profit is ₹40,000, find A’s total earning. (a) ₹16,200 (b) ₹18,000 (c) ₹14,400 (d) ₹19,800

B29. [Continued Ratio, Three-Part Sum] The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3, and the ratio of the second to the third is 5 : 8, find the second number. (a) 28 (b) 32 (c) 35 (d) 30

B30. [Age Ratio, Past and Future Combined] The ratio of the ages of a father and his son, 4 years ago, was 5 : 2. Four years from now, the ratio of their ages will be 3 : 2. Find the father’s present age. (a) 14 years (b) 18 years (c) 16 years (d) 20 years