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In a tour, I spent every day as many ten-rupee notes as the number of days I had been away from the home. My total expenditure was 18,300. How long did I stay away from home? - Mathematics

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MCQ

In a tour, I spent every day as many ten-rupee notes as the number of days I had been away from the home. My total expenditure was 18,300. How long did I stay away from home?

Options

  • 1 month

  • 2 months

  • 3 months

  • 4 months

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Solution

2 months

Explanation:

Let man spend ₹ 10, 20, 30 ...........

On 1st 2nd 3rd ....... day respectively

ATQ

10 + 20 + 30 .............=18300

`"S"_"n"="n"/2(2"a"+("n"-1)"d")`

`"n"/2(2(10)+("n"-1)10)=18300`

`"n"/2[10"n"+10]=18300`

5n2 + 5n = 18300

n2 + n − 3660 = 0

n2 + 61n − 60n − 3660 = 0

n (n + 61) − 60(n + 61) = 0

(n − 60) (n + 61) = 0, n = 60, n ≠ 61

n = 60
i.e. 2 months

Concept: Series and Equations (Entrance Exam)
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