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A boy agrees to work at the rate of one rupee on the 
first day, two rupees on the second day, and four rupees on third day and so on. How much will the boy get if he started working on the 1st of February and finishes on the 20th of February?
a) 2^20
b) 2^20-1
c) 2^19-1
d) 2^19
e) None of these
Correct answer is option 'B'. Can you explain this answer?
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A boy agrees to work at the rate of one rupee on thefirst day, two rup...
To find out how much the boy will get if he starts working on the 1st of February and finishes on the 20th of February, we need to calculate the sum of the money he earns each day.

The pattern of his earnings is as follows:
Day 1: 1 rupee
Day 2: 2 rupees
Day 3: 4 rupees
Day 4: 8 rupees
Day 5: 16 rupees
...
Day n: 2^(n-1) rupees

We can observe that the amount he earns each day is double the amount he earned on the previous day. So we can write the general formula for his earnings on day n as 2^(n-1) rupees.

Now let's calculate his earnings for the 20 days:

Day 1: 1 rupee
Day 2: 2 rupees
Day 3: 4 rupees
Day 4: 8 rupees
Day 5: 16 rupees
Day 6: 32 rupees
Day 7: 64 rupees
Day 8: 128 rupees
Day 9: 256 rupees
Day 10: 512 rupees
Day 11: 1024 rupees
Day 12: 2048 rupees
Day 13: 4096 rupees
Day 14: 8192 rupees
Day 15: 16384 rupees
Day 16: 32768 rupees
Day 17: 65536 rupees
Day 18: 131072 rupees
Day 19: 262144 rupees
Day 20: 524288 rupees

To find the total earnings, we need to sum up all these amounts:

Total earnings = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096 + 8192 + 16384 + 32768 + 65536 + 131072 + 262144 + 524288

This is a geometric series with a common ratio of 2 and 20 terms. We can use the formula for the sum of a geometric series to calculate the total earnings.

Sum = (first term * (1 - common ratio^n)) / (1 - common ratio)

Plugging in the values, we get:

Sum = (1 * (1 - 2^20)) / (1 - 2)
Sum = (1 * (1 - 1048576)) / -1
Sum = (1 * -1048575) / -1
Sum = 1048575

Therefore, the boy will get a total of 1048575 rupees if he starts working on the 1st of February and finishes on the 20th of February.

But the given options do not match the calculated amount. So none of the given options is correct.
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A boy agrees to work at the rate of one rupee on thefirst day, two rupees on the second day, and four rupees on third day and so on. How much will the boy get if he started working on the 1st of February and finishes on the 20th of February?a) 2^20b) 2^20-1c) 2^19-1d) 2^19e) None of theseCorrect answer is option 'B'. Can you explain this answer?
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