The average number of pages typed by a typist on Monday, Tuesday and Wednesday is 39. The average number of pages typed by a typist on Tuesday, Wednesday and Thursday is 26. If the typist typed 36 pages on Thursday, the number of pages typed by him on Thursday is what percent less than that on Monday?

Options

A. 48
B. 54
C. 52
D. 44

Answer

To solve the problem step-by-step, we will follow these calculations:

### Step 1: Calculate the total pages typed on Monday, Tuesday, and Wednesday
Given the average number of pages typed on Monday, Tuesday, and Wednesday is 39, we can use the formula for average:

\[ \text{Average} = \frac{\text{Total Pages}}{\text{Number of Days}} \]

Let \( M \) be the number of pages typed on Monday, \( T \) on Tuesday, and \( W \) on Wednesday. We have:

\[ \frac{M + T + W}{3} = 39 \]

Multiplying both sides by 3 gives:

\[ M + T + W = 117 \]

### Step 2: Calculate the total pages typed on Tuesday, Wednesday, and Thursday
Given the average number of pages typed on Tuesday, Wednesday, and Thursday is 26, we can use the same formula:

\[ \frac{T + W + Th}{3} = 26 \]

Let \( Th \) be the number of pages typed on Thursday. Multiplying both sides by 3 gives:

\[ T + W + Th = 78 \]

### Step 3: Substitute the known value for Thursday
We know that the typist typed 36 pages on Thursday:

\[ Th = 36 \]

Substituting this into the equation from Step 2:

\[ T + W + 36 = 78 \]

Subtracting 36 from both sides gives:

\[ T + W = 42 \]

### Step 4: Find the number of pages typed on Monday
Now we have two equations:
1. \( M + T + W = 117 \)
2. \( T + W = 42 \)

We can substitute \( T + W \) from the second equation into the first:

\[ M + 42 = 117 \]

Subtracting 42 from both sides gives:

\[ M = 75 \]

### Step 5: Calculate the percentage decrease from Monday to Thursday
Now we know:
- Pages typed on Monday \( M = 75 \)
- Pages typed on Thursday \( Th = 36 \)

To find the percentage decrease from Monday to Thursday, we use the formula:

\[ \text{Percentage Decrease} = \frac{M - Th}{M} \times 100 \]

Substituting the values:

\[ \text{Percentage Decrease} = \frac{75 - 36}{75} \times 100 = \frac{39}{75} \times 100 \]

Calculating this gives:

\[ \text{Percentage Decrease} = 52\% \]

### Final Answer
The number of pages typed on Thursday is 52% less than that on Monday.

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