On January 1, Ashutosh opened a current account by investing $300. On each of 8th January and 15th January, he invested $n on that account. However, on 22nd January he withdrew $250 from the account due to an emergency need. If the balance on that account at the end of 31st January was $300, and the average balance for each day was also $300, then what is the approximate value of n?
Is it just me? or does this question feel inconsistent with itself (red portion)?
Anyways, here is how I arrived at the answer:
Balance from Jan 1 to 7 (7 DAYS)= 300
Jan 8 to 14 (7 DAYS) = 300 + n
Jan 15 to 21 (7 DAYS) = 300 + n + n = 300 + 2n
Jan 22 to 31 (10 DAYS) = 300 + 2n - 250 = 50 + 2n
Total of each days balance = 7*300 + 7*(300+n) + 7*(300+2n) + 10*(50+2n)
=2100 + 2100 + 7n + 2100 + 14n + 500 + 20n
= 6800 + 41n
Also, Average balance per day = 300
So, Total of each days balance/31 = 300
Total of each days balance = 9300
6800 + 41n = 9300
41n = 2500
n = 2500/41 = approx 60.97... = approx 61
Question is asking for approximate value.
Answer: C - 61
PS: If we consider that balance at end of 31st jan was 300, then it would mean that 50+2n = 300; 2n = 250; n = 125... This appears to be inconsistent with the above answer, also, it is not reflected in any of the options, so this information was ignored by me. Did I miss anything?