Practice Questions
Concept Explanation
When a fixed payment is shared, each worker's wage is proportional to work done.
Key Formulas
- Wage share = (Individual rate / Sum of rates) × Total wage
- Work done = Rate × Time; if time is equal, wages follow efficiency ratio
- If A is twice as efficient as B, wage ratio A:B = 2:1 for equal time
Example
A and B finish work worth Rs. 1,200 together. A alone takes 12 days, B alone 18 days. Ratio of rates = 3:2. A gets Rs. 720, B gets Rs. 480.
Common Trap
Use work rates, not days directly. Fewer days means higher rate and larger wage share.
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Q1 Easy
A can finish a work in 12 days and B can finish the same work in 18 days. If they work together on the work, in what ratio should their wages be divided?
ExplanationWages are divided in the ratio of their work rates: 1/12 : 1/18 = 3:2. -
Q2 Easy
A and B complete the work together and receive Rs. 900 in total. If their efficiencies are in the ratio 2:1, how much should A receive?
ExplanationA's share = 2/3 × 900 = Rs. 600. -
Q3 Hard
A, B and C finish the work together and receive Rs. 2,400. If their daily work rates are 1/6, 1/8 and 1/12 respectively, how much should A receive?
ExplanationRate ratio = 4:3:2. A's share = 4/9 × 2400 = Rs. 960. -
Q4 Medium
A can finish a work in 10 days and B can finish it in 15 days. They work together and receive Rs. 1,250. How much should B receive?
ExplanationB's share = (1/15)/(1/10 + 1/15) × 1250 = Rs. 500. -
Q5 Easy
A and B work for the same number of days on the work. A does twice as much work as B in that time. If Rs. 1,800 is paid for the work, how much should A receive?
ExplanationWork ratio A:B = 2:1. A receives 2/3 × 1800 = Rs. 1,200. -
Q6 Easy
A and B work at the same daily rate on the work. A works for 8 days and B works for 12 days. In what ratio should their wages be divided?
ExplanationSame rate means wages follow days worked: 8:12 = 2:3. -
Q7 Medium
A can finish a work in 8 days and B can finish it in 12 days. They work together and receive Rs. 2,000. How much should A receive?
ExplanationA's share = (1/8)/(1/8 + 1/12) × 2000 = Rs. 1,200.
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Q8 Easy
Three workers receive Rs. 3,600 for the work and their wages are divided in the ratio 2:3:5. What is the largest share?
ExplanationLargest share = 5/10 × 3600 = Rs. 1,800. -
Q9 Medium
A can finish a work in 6 days and B can finish it in 12 days. They work together and receive Rs. 900. How much should A receive?
ExplanationRate ratio A:B = 2:1. A receives 2/3 × 900 = Rs. 600. -
Q10 Medium
A, B and C receive Rs. 1,440 for the work. If their work rates are in the ratio 3:4:5, how much should C receive?
ExplanationC's share = 5/12 × 1440 = Rs. 600. -
Q11 Hard
A earns Rs. 800 for 4 days of work and B earns Rs. 900 for 6 days of work on the same type of work. What is the ratio of their daily wages?
ExplanationA's daily wage = Rs. 200 and B's daily wage = Rs. 150. Ratio = 4:3. -
Q12 Hard
A can finish a work in 20 days and B can finish it in 30 days. They work together and receive Rs. 2,500. What is the difference between A's wage and B's wage?
ExplanationA receives Rs. 1,500 and B receives Rs. 1,000. Difference = Rs. 500. -
Q13 Medium
A and B work for the same number of days on the work. A is three times as efficient as B. If the total payment is Rs. 1,600, how much should B receive?
ExplanationWage ratio A:B = 3:1. B receives 1/4 × 1600 = Rs. 400. -
Q14 Easy
A completes 2/5 of the work and B completes 3/5 of the same work. If the total payment is Rs. 1,500, how much should B receive?
ExplanationB's share = 3/5 × 1500 = Rs. 900.
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DS1 Easy
How much should A receive as his wage share?
Statement IA alone can finish the work in 12 days and B alone in 18 days.
Statement IIThe total wage for the work is Rs. 1,200.
ExplanationBoth the rate ratio and total wage are needed: A receives 3/5 × 1200 = Rs. 720. -
DS2 Easy
How much should B receive from the total wage of Rs. 900?
Statement IA and B work for the same time and their efficiencies are in the ratio 2:1.
Statement IIThe total wage for the work is Rs. 900.
ExplanationTogether: B receives 1/3 × 900 = Rs. 300.
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DS3 Easy
In what ratio should the wages of A and B be divided?
Statement IA alone can finish the work in 10 days.
Statement IIB alone can finish the work in 15 days.
ExplanationTheir work rates are 1/10 and 1/15, so the wage ratio is 3:2. -
DS4 Medium
Does A receive more than Rs. 500?
Statement IA alone can finish the work in 8 days and B alone in 24 days.
Statement IIThe total wage for the work is Rs. 1,000.
ExplanationA receives (1/8)/(1/8 + 1/24) × 1000 = Rs. 750, which is more than Rs. 500.