A can complete 50% of a job in 9 days and B can complete 25% of the job in 9 days if they worked alone. If they worked together how much of the job (in %) can they complete in 9 days?

Options

A. 80
B. 90
C. 75
D. 100

Answer

To solve the problem step by step, we will first determine the work rates of A and B, and then combine their efforts to find out how much work they can complete together in 9 days.

### Step 1: Determine A's Work Rate
A can complete 50% of the job in 9 days. Therefore, in 9 days, A completes:
\[ \text{Work done by A in 9 days} = 50\% \]
To find A's work rate per day, we can express this as:
\[ \text{Work rate of A} = \frac{50\%}{9 \text{ days}} = \frac{50}{9}\% \text{ per day} \]

### Step 2: Determine B's Work Rate
B can complete 25% of the job in 9 days. Therefore, in 9 days, B completes:
\[ \text{Work done by B in 9 days} = 25\% \]
To find B's work rate per day, we can express this as:
\[ \text{Work rate of B} = \frac{25\%}{9 \text{ days}} = \frac{25}{9}\% \text{ per day} \]

### Step 3: Combine A's and B's Work Rates
Now, we will combine A's and B's work rates to find out how much work they can do together in one day:
\[ \text{Combined work rate} = \text{Work rate of A} + \text{Work rate of B} \]
Substituting the values we found:
\[ \text{Combined work rate} = \frac{50}{9}\% + \frac{25}{9}\% = \frac{50 + 25}{9}\% = \frac{75}{9}\% \text{ per day} \]

### Step 4: Calculate the Total Work Done in 9 Days
To find out how much work A and B can complete together in 9 days, we multiply their combined work rate by 9:
\[ \text{Total work in 9 days} = \text{Combined work rate} \times 9 \]
Substituting the combined work rate:
\[ \text{Total work in 9 days} = \frac{75}{9}\% \times 9 = 75\% \]

### Final Answer
Thus, A and B together can complete **75%** of the job in 9 days.

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