Question

A can do a work in 18 days. A and B both together can do the same work in 11 days. Then, in one day, B alone can do

• A. 13/198 part of the work
• B. 7/198 part of the work
• C. 15/198 part of the work
• D. 17/198 part of the work

Hint:

The shortcut for finding B's rate is: \[ \frac{\text{Difference in days}}{\text{Product of days}} = \frac{18 - 11}{18 \times 11} = \frac{7}{198} \]

Answer 1

The Correct Option is B

Concept: In time and work problems, the "Work Rate" of a person is the reciprocal of the total time they take to finish the work. If $W$ is the total work, the work done in one day is $1/\text{Time}$.

Step 1: Calculate individual and combined work rates.

• A's 1-day work = $\frac{1}{18}$
• (A + B)'s 1-day work = $\frac{1}{11}$

Step 2: Set up the equation for B's work rate.
Let B's 1-day work be $x$. The sum of A's rate and B's rate equals their combined rate: \[ \text{A's rate} + \text{B's rate} = \text{Combined rate} \] \[ \frac{1}{18} + x = \frac{1}{11} \] \[ x = \frac{1}{11} - \frac{1}{18} \]

Step 3: Solve the subtraction of fractions.
To subtract these, we find a common denominator: \[ \text{Common Denominator} = 11 \times 18 = 198 \] \[ x = \frac{18 - 11}{198} \] \[ x = \frac{7}{198} \] Thus, B can do $7/198$ part of the work in one day. Final Answer: Option B