A man saves RS. 200 in each of the first 3 months of his service. In each of the subsequent month his saving increases by RS. 40 more than the saving of immediately previous months. His total saving from the start of service will be RS. 11040 after how many months?

Asked by aliencpr31 | 26th Jul, 2019, 10:03: AM

Expert Answer:

For 1st 3 months, amount = 600 Rs.
For the 4th month, amount saved is 240 Rs.
And then the saved amount increases by 40 every month
So, they form an A.P. with first term a=240 and common difference d=40
We know that, sum of n first n terms of an A.P. is
S subscript n equals n over 2 open parentheses 2 a plus left parenthesis n minus 1 right parenthesis d close parentheses
S u b t r a c t i n g space 600 space f r o m space t o t a l space a m o u n t space g i v e s space 10440 space R s.
rightwards double arrow 10440 equals n over 2 open parentheses 480 plus left parenthesis n minus 1 right parenthesis 40 close parentheses
rightwards double arrow n squared plus 11 n minus 522 equals 0
rightwards double arrow left parenthesis n plus 29 right parenthesis left parenthesis n minus 18 right parenthesis equals 0
rightwards double arrow n equals negative 29 space o r space 18
N o. space o f space m o n t h s space c a n apostrophe t space b e space n e g a t i v e comma space t h e r e f o r e space n equals 18
H e n c e comma space a space m a n space s a v e s space R s. space 11040 space a f t e r space 18 plus 3 equals 21 space m o n t h s.

Answered by Renu Varma | 26th Jul, 2019, 12:14: PM

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