Amit and Sujit together can complete an assignment of data entry in five days . Sujit's speed is 80% of Amit's speed and the total key depressions in the assignment are 5,76,000. what is Amit's speed in key depressions per hour if they work for 8 hours a day ?

Options

A. 4800
B. 6400
C. 8000
D. 7200

Explanation

To solve the problem, we need to find Amit's speed in key depressions per hour. Let's break it down step by step.

### Step 1: Determine the total work done in key depressions.
The total key depressions in the assignment are given as 5,76,000.

### Step 2: Calculate the total work done per day.
Since Amit and Sujit together can complete the assignment in 5 days, we can find out how much work they do in one day:
\[ \text{Work done per day} = \frac{\text{Total Key Depressions}}{\text{Total Days}} = \frac{5,76,000}{5} = 1,15,200 \text{ key depressions per day} \]

### Step 3: Set up the relationship between Amit's and Sujit's speeds.
Let Amit's speed be \( A \) key depressions per hour. Since Sujit's speed is 80% of Amit's speed, we can express Sujit's speed as:
\[ S = 0.8A \]

### Step 4: Calculate the combined speed of Amit and Sujit.
The combined speed of Amit and Sujit when they work together is:
\[ \text{Combined Speed} = A + S = A + 0.8A = 1.8A \]

### Step 5: Calculate the total work done in a day using their combined speed.
Since they work for 8 hours a day, the total work done by both in one day can also be expressed as:
\[ \text{Work done in a day} = \text{Combined Speed} \times \text{Hours Worked} = 1.8A \times 8 \]
Setting this equal to the work done per day from Step 2:
\[ 1.8A \times 8 = 1,15,200 \]

### Step 6: Solve for Amit's speed \( A \).
Now, we can solve for \( A \):
\[ 14.4A = 1,15,200 \]
\[ A = \frac{1,15,200}{14.4} = 8,000 \text{ key depressions per hour} \]

### Conclusion:
Amit's speed is \( 8,000 \) key depressions per hour.

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