Question

A man saved Rs 200 during the first month, Rs 225 in the second month and in this way he increases his savings by Rs 25 every month. Find in what time his savings will be Rs 13325.

Answer 1

Answer :

A man saves Rs 200 in very first month and he saves Rs 25 more in every next month.

Suppose it takes n number of months to save Rs 13325.

So according to the situation,we get the sequence of his savings as,

200,225,250,275,.......................13325
Here in the above arithmetic sequence,
First term, a=200
Common difference,d=25
Sum of the given series,S = 13325

We know that,
Sum of an arithmetic sequence is,

S = (n/2) { 2a + (n - 1)d}

=> 13325 = (n/2){ 2×200 + (n - 1)×25}

=> 13325 = (n/2) { 400 + (n - 1)×25}

=> 13325 = (n/2) (400 - 25 + 25n)

=> 13325 × 2 = n(25n +375)

=> 25 n^2 + 375 n = 26650

=> n^2 + 15 n - 1066 = 0

=> n^2 + 41n - 26n - 1066 = 0

=> n(n + 41) -26 (n + 41)

=> (n - 26) (n + 41) = 0

=> n = 26 or n = - 41

Since n is the number of months it takes to collect Rs 13325,so it can not be negative.

● So in 26 months,that man will save Rs 13325.


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