Kavita a student of IIMA, told me that she did everyday 3 more passages of English than that of previous day and thus she completed all the passages in 10 days. Later on she told me that the number of passages she did on the last but one day were four times that she did on the second day :
Number of passages she has done on the last day

Options

A. A. 30
B. B. 41
C. C. 32
D. D. none of these

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define the variables
Let the number of passages Kavita did on the first day be \( a \).

### Step 2: Write the number of passages for each day
Since Kavita did 3 more passages each day than the previous day, we can express the number of passages she did on each day as follows:
- Day 1: \( a \)
- Day 2: \( a + 3 \)
- Day 3: \( a + 6 \)
- Day 4: \( a + 9 \)
- Day 5: \( a + 12 \)
- Day 6: \( a + 15 \)
- Day 7: \( a + 18 \)
- Day 8: \( a + 21 \)
- Day 9: \( a + 24 \)
- Day 10: \( a + 27 \)

### Step 3: Express the last day’s passages
From the above, we can see that on the last day (Day 10), the number of passages she did is:
\[ L = a + 27 \]

### Step 4: Use the information about the second day
We know that the number of passages she did on the last but one day (Day 9) is four times the number of passages she did on the second day. The number of passages on Day 9 is:
\[ a + 24 \]
The number of passages on Day 2 is:
\[ a + 3 \]
According to the problem:
\[ a + 24 = 4(a + 3) \]

### Step 5: Solve the equation
Now, we will solve the equation:
\[ a + 24 = 4(a + 3) \]
Expanding the right side:
\[ a + 24 = 4a + 12 \]
Now, rearranging the equation:
\[ 24 - 12 = 4a - a \]
\[ 12 = 3a \]
\[ a = 4 \]

### Step 6: Find the number of passages on the last day
Now that we have \( a \), we can find the number of passages on the last day:
\[ L = a + 27 = 4 + 27 = 31 \]

### Final Answer
The number of passages Kavita did on the last day is **31**.

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