A person saves each year Rs 100 more than he saved in the

Question

A person saves each year Rs 100 more than he saved in the preceding year, and he saves Rs 200 the first year. How many years would it take for his savings, not including interest, to amount to Rs 23000 ?

Don't have the answer choices.

Don't have the answer choices.

Anonym · Answer

This is an evenly spaced set.

For evenly spaced set you can apply the formula to find the sum, which is:
 \frac{(First Term + Last Term)}{2}  times the Total Number of terms.

Let n be the total number of terms (or total no. of years for this question)
As we don't have the last term we'll have to make do with this as the last term:  (n-1)*100+200  (as every term increase by 100 from the preceding one, and the first term is 200. Take note that n is also the last term)

Algebra equation:
 23000=n*\frac{200+ }{2} 
 23000=n*\frac{200+(100n-100+200)}{2} 
.....
end up with this
 n^2+3n-460=0  (could have used the answer choices to test which one fits)
 (n+23)(n-20)=0

n={-23,20}

As n cannot be negative, so the answer is 20.

GyanOne · Answer

At the end of the 1st year, his savings = 200 
At the end of the 2nd year, his savings = 300
At the end of the 3rd year, his savings = 400

This is clearly an AP. If there are n terms in this, 
23000 = (n/2)  
=> 46000 = 100n^2 + 300n
=> n^2 + 3n - 460 = 0
=> n^2 + 23n - 20n - 460 = 0
=> (n+23) (n-20)=0
=> n = 20

Therefore it will take 20 years for the savings to add up to at least 23,000.

kraizada84 · Answer

its AP
Sum to n terms=Sn =23000= n/2{300+n*100}
=>460=n*(3+n)=20*23

n=20

boomtangboy · Answer

Ok I have one question why is the interest earned by d guy ignored. I feel the question is incomplete

Posted from my mobile device

kraizada84 · Answer

there might be the case the guy saves at home NOT at any bank OR he saves such that no interest he gets. anyways the question states and we do, thats it, no need to worry about his interest..

BrushMyQuant · Answer

Please tag sequence
Thank you

achloes · Answer

BrushMyQuant   gmatophobia

I'm using the sequences formula but not getting n=20.

an = a1 + (n – 1)d
23000 = 200 + (n-1) 100 
23000 = 200 + 100n - 100
23000 - 200 + 100 = 100n 
100n = 22900 
n = 229

What am I doing wrong?

gmatophobia · Answer

Hey  achloes

You've found the number of years it will take for the person to deposit Rs 23000.

However, we don't want after how many years the person will deposit Rs. 23000; We want after how many years the person will have a net savings of Rs 23000.

For example-

John saves $1 more than the previous day and he starts his savings on the first day with $1. We want to find out after how many days John will have saved $10

Day 1:  $1 
Day 2: $1 +  $2  = $3
Day 3: $1 + $2 +  $3  = $6
Day 4: $1 + $2 + $3 +  $4  = $10

The bolded values are the deposits made by John on that day. As we can see that at the end of the fourth day, John will have a saving of $10.

Note : John isn't depositing $10 on the fourth day, but the cumulative savings is $10 on the fourth day.

A person saves each year Rs 100 more than he saved in the

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