A can do a work in 25 days, B in 30 days, and C in 50 days. If A and B work toge

₹0.0

Question: A can do a work in 25 days, B in 30 days, and C in 50 days. If A and B work together for 10 days, how much of the work is completed?

Options:

Correct Answer: 1/4

Solution:

Combined rate of A and B = (1/25 + 1/30) = 11/150. In 10 days, they complete 11/15 of the work.

A can do a work in 25 days, B in 30 days, and C in 50 days. If A and B work together for 10 days, how much of the work is completed?

A can do a work in 25 days, B in 30 days, and C in 50 days. If A and B work together for 10 days, how much of the work is completed?

Step 1: Determine the work rate of A. A can complete the work in 25 days, so A's work rate is 1/25 of the work per day.
Step 2: Determine the work rate of B. B can complete the work in 30 days, so B's work rate is 1/30 of the work per day.
Step 3: Add the work rates of A and B to find their combined work rate. This is done by calculating (1/25 + 1/30).
Step 4: To add the fractions, find a common denominator. The least common multiple of 25 and 30 is 150.
Step 5: Convert the fractions: 1/25 = 6/150 and 1/30 = 5/150.
Step 6: Now add the two fractions: 6/150 + 5/150 = 11/150. This is the combined work rate of A and B.
Step 7: Calculate how much work A and B complete in 10 days. Multiply their combined work rate (11/150) by 10 days: (11/150) * 10 = 110/150.
Step 8: Simplify 110/150 to find the fraction of work completed. This simplifies to 11/15.

Work Rate Calculation – Understanding how to calculate the work rate of individuals and combine their rates to determine total work done over a period.
Fraction Addition – Adding fractions to find a combined work rate, which is essential for solving problems involving multiple workers.
Time and Work Problem Solving – Applying the concept of time and work to determine how much work is completed in a given timeframe.