Question

A can complete a work in 15 days and B can complete the same work in 10 days. In how many days will they complete the work together?

• A. 5 days
• B. 6 days
• C. 7.5 days
• D. 8 days

Hint:

You can also use the LCM method to avoid working with fractional steps! Assume the total work is the LCM of 15 and 10, which is 30 units. Efficiency of A = $\frac{30}{15} = 2$ units/day. Efficiency of B = $\frac{30}{10} = 3$ units/day. Combined efficiency of A + B = $2 + 3 = 5$ units/day. Total days needed = $\frac{30 \text{ total units}}{5 \text{ units/day}} = 6$ days.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Time and work problems determine how individual efficiencies combine when people work together. The daily rate of work done by an individual is the reciprocal of the total days they require to complete the job on their own. When working simultaneously, their individual daily efficiencies are added together to find their combined daily work rate.

Step 2: Key Formula or Approach:
If A can complete a job in $x$ days and B in $y$ days, the time taken ($T$) by both working together can be evaluated directly using the product-over-sum formula: $$T = \frac{x \times y}{x + y}$$

Step 3: Detailed Explanation:
Given rates from the question statement: Time taken by A ($x$) = 15 days Time taken by B ($y$) = 10 days Substitute these values into the combined time formula: \[ T = \frac{15 \times 10}{15 + 10} \] \[ T = \frac{150}{25} \] Dividing 150 by 25 yields: \[ T = 6 \text{ days} \]

Step 4: Final Answer:
They will complete the work together in 6 days.