Question 1

Two painters, Raj and Priya, can paint a wall together in 10 days. Raj's daily wage is ₹800 and Priya's daily wage is ₹1,200. If they work together for 10 days and receive a total payment of ₹20,000, how much does Priya earn?

Accepted Answer

Step 1: Raj's daily wage : Priya's daily wage = 800 : 1,200 = 2 : 3 (dividing by 400). Step 2: Since both work the same number of days (10), payment is distributed in the ratio of daily wages. Step 3: Total parts = 2 + 3 = 5. Step 4: Priya's share = (3/5) × 20,000 = ₹12,000.

Question 2

A and B together can complete a piece of work in 12 days. If A's daily wage is ₹500 and B's daily wage is ₹300, and they are paid in the ratio of work done, how much will B earn if the total payment for the work is ₹9,600?

Accepted Answer

Step 1: A and B work together for 12 days. Step 2: Since both work the same number of days (12), the work done is proportional to their daily wages. Step 3: Ratio of work done = Ratio of daily wages = 500:300 = 5:3. Step 4: B's share = (3/8) × 9,600 = ₹3,600.

Question 3

A contractor hires two workers. Worker M earns ₹400 per day and Worker N earns ₹600 per day. If M works for 10 days and N works for 8 days on the same project, what is the ratio of their total earnings?

Accepted Answer

Step 1: M's total earnings = 400 × 10 = ₹4,000. Step 2: N's total earnings = 600 × 8 = ₹4,800. Step 3: Ratio = 4,000 : 4,800 = 5 : 6 (dividing by 800).

Question 4

Three workers A, B, and C are paid ₹1,200, ₹1,500, and ₹1,800 respectively per day. If they work together for 8 days and complete a project, and payment is distributed based on daily wages, what is A's share of the total payment of ₹28,800?

Accepted Answer

Step 1: A's daily wage = ₹1,200, B's daily wage = ₹1,500, C's daily wage = ₹1,800. Step 2: Ratio of daily wages = 1,200 : 1,500 : 1,800 = 4 : 5 : 6 (dividing by 300). Step 3: Total parts = 4 + 5 + 6 = 15. Step 4: A's share = (4/15) × 28,800 = ₹7,680.

Question 5

A drain pipe can empty a full cistern in 20 hours. If the cistern is already 3/4 full and the drain is opened, how long will it take to empty it completely?

Accepted Answer

Step 1: The drain empties the entire cistern in 20 hours. Step 2: To empty 3/4 of the cistern, time required = (3/4) × 20 = 15 hours.

Question 6

If 8 workers can build a wall in 15 days, how many days will 12 workers take to build the same wall, assuming all workers work at the same rate?

Accepted Answer

Step 1: Total work = 8 workers × 15 days = 120 worker-days. Step 2: With 12 workers, days needed = 120 ÷ 12 = 10 days.

Question 7

The efficiency of X is 25% more than Y. If X and Y together can complete a project in 10 days, in how many days can X alone complete the project?

Accepted Answer

Step 1: Let Y's efficiency = 100 units/day, then X's efficiency = 125 units/day. Step 2: Combined efficiency = 100 + 125 = 225 units/day. Step 3: Total work = 225 × 10 = 2250 units. Step 4: X's time alone = 2250 ÷ 125 = 18 days.

Question 8

A contractor hires 8 workers to complete a job in 15 days. After 5 days, 2 workers leave. How many additional days will it take to complete the remaining work?

Accepted Answer

Step 1: Total work = 8 workers × 15 days = 120 worker-days. Step 2: Work completed in 5 days = 8 × 5 = 40 worker-days. Step 3: Remaining work = 120 - 40 = 80 worker-days. Step 4: Remaining workers = 8 - 2 = 6. Step 5: Additional days needed = 80 ÷ 6 = 13.33 days ≈ 13⅓ days.

Question 9

Pipe A can fill a cistern in 12 hours, and Pipe B can empty it in 18 hours. If both pipes are opened simultaneously, how long will it take to fill the cistern?

Accepted Answer

Step 1: Rate of Pipe A = 1/12 per hour (filling). Step 2: Rate of Pipe B = 1/18 per hour (emptying). Step 3: Net rate = 1/12 - 1/18 = (3-2)/36 = 1/36 per hour. Step 4: Time to fill = 1 ÷ (1/36) = 36 hours.

Question 10

Two partners, P and Q, start a business. P invests capital and works full-time, while Q only invests capital without working. Their profit is to be divided in the ratio of capital invested. However, P is also entitled to a salary of ₹5000 per month for his work. In a year, if the total profit (before P's salary) is ₹180,000 and P's capital is ₹3,00,000 while Q's capital is ₹2,00,000, what is Q's share of the profit after P receives his salary?

Accepted Answer

Step 1: P's annual salary = ₹5000 × 12 = ₹60,000. Step 2: Profit after salary = ₹180,000 - ₹60,000 = ₹120,000. Step 3: Capital ratio P:Q = 3,00,000 : 2,00,000 = 3:2. Step 4: Q's share of remaining profit = (2/(3+2)) × ₹120,000 = (2/5) × ₹120,000 = ₹48,000.

Question 11

A contractor hired 60 workers to complete a road in 45 days. After 15 days, he realized that only 1/4 of the work was done. How many additional workers must he hire to complete the remaining work in the stipulated time?

Accepted Answer

Step 1: Initial plan: 60 workers × 45 days = 2700 worker-days for full work. Step 2: Work done in 15 days = 1/4. Step 3: Actual worker-days used = 60 × 15 = 900. Step 4: Rate of work = (1/4) / 900 = 1/3600 of work per worker-day. Step 5: Remaining work = 3/4. Step 6: Remaining days = 45 - 15 = 30 days. Step 7: Worker-days needed for remaining work = (3/4) / (1/3600) = (3/4) × 3600 = 2700. Step 8: Workers needed = 2700 / 30 = 90 workers. Step 9: Additional workers = 90 - 60 = 30 workers.

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