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If Ajit saves Rs. 400 more each year than he did the year before and if he saves Rs. 2000 in the first year, after how many years will his savings be more than Rs.100000 altogether?
- a)19 years
- b)20 years
- c)21 years
- d)18 years
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If Ajit saves Rs. 400 more each year than he did the year before and i...
We need the sum of the series 2000 + 2400 + 2800 to cross 100000.
Trying out the options, we can see that in 20 years the sum of his savings would be: 2000 + 2400 + 2800 +…+ 9600.
The sum of the series would be 20 × 5800 = 116000.
If we remove the 20th year we will get the saving for 19 years.
The series would be 2000 + 2400 + 2800 + … + 9200. Sum of the series would be 116000 − 9600 = 106400.
If we remove the 19th year’s savings the savings would be 106400 − 9200 which would go below 100000.
Thus, after 19 years his savings would cross 100000. Option (a) is correct
Trying out the options, we can see that in 20 years the sum of his savings would be: 2000 + 2400 + 2800 +…+ 9600.
The sum of the series would be 20 × 5800 = 116000.
If we remove the 20th year we will get the saving for 19 years.
The series would be 2000 + 2400 + 2800 + … + 9200. Sum of the series would be 116000 − 9600 = 106400.
If we remove the 19th year’s savings the savings would be 106400 − 9200 which would go below 100000.
Thus, after 19 years his savings would cross 100000. Option (a) is correct
Most Upvoted Answer
If Ajit saves Rs. 400 more each year than he did the year before and i...
Solution:
Let us assume that Ajit saves x amount in the second year.
So, Ajit will save (x+400) amount in the third year.
Similarly, Ajit will save (x+800) amount in the fourth year.
Hence, Ajit's savings will be in the following sequence:
Year 1: Rs. 2000
Year 2: Rs. x + 2000
Year 3: Rs. x + 2400
Year 4: Rs. x + 3200
Year 5: Rs. x + 4000
and so on...
We can see that Ajit's savings are increasing by Rs. 400 every year.
Now, we need to find after how many years Ajit's savings will be more than Rs. 100000 altogether.
Let us assume that Ajit's savings will be more than Rs. 100000 after n years.
So, we can write the following equation:
2000 + (x + 2000) + (x + 2400) + (x + 3200) + ... + (x + 400(n-1)) > 100000
Simplifying the above equation, we get:
2000n + 400n(n-1)/2 > 98000
Solving the above equation, we get:
n > 18.5
Since n has to be a whole number, Ajit's savings will be more than Rs. 100000 after 19 years.
Therefore, the correct answer is option A.
Let us assume that Ajit saves x amount in the second year.
So, Ajit will save (x+400) amount in the third year.
Similarly, Ajit will save (x+800) amount in the fourth year.
Hence, Ajit's savings will be in the following sequence:
Year 1: Rs. 2000
Year 2: Rs. x + 2000
Year 3: Rs. x + 2400
Year 4: Rs. x + 3200
Year 5: Rs. x + 4000
and so on...
We can see that Ajit's savings are increasing by Rs. 400 every year.
Now, we need to find after how many years Ajit's savings will be more than Rs. 100000 altogether.
Let us assume that Ajit's savings will be more than Rs. 100000 after n years.
So, we can write the following equation:
2000 + (x + 2000) + (x + 2400) + (x + 3200) + ... + (x + 400(n-1)) > 100000
Simplifying the above equation, we get:
2000n + 400n(n-1)/2 > 98000
Solving the above equation, we get:
n > 18.5
Since n has to be a whole number, Ajit's savings will be more than Rs. 100000 after 19 years.
Therefore, the correct answer is option A.
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If Ajit saves Rs. 400 more each year than he did the year before and if he saves Rs. 2000 in the first year, after how many years will his savings be more than Rs.100000 altogether?a)19 yearsb)20 yearsc)21 yearsd)18 yearsCorrect answer is option 'A'. Can you explain this answer?
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