A customer pays ₹975 in installments. The payment is done each month for ₹5 less than the previous month. If the first installment is ₹100, how much time will be taken to pay the entire amount?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 15 months.
First term (a) = 100
Common difference (d) = - 5 (since each installment is ₹5 less)
Sum of the series (S) = 975
S = (n/2)[2a + (n - 1)d] where n is the number of terms (or months in this case)
⇒ 975 = (n/2)[2(100) + (n - 1)(-5)]
⇒ 975 = (n/2)(200 - 5n + 5)
⇒ 1950 = n(205 - 5n)
⇒ 1950 = 205n - 5n2
⇒ 5n2 - 205n + 1950 = 0
⇒ n2 - 41n + 390 = 0
⇒ (n - 15)(n - 26) = 0
⇒ n = 15 or n = 26
15th term = 100 + (15 - 1)(-5) = 30
26th term = 100 + (26 - 1)(-5) = -25 (not valid)
Therefore, it will take 15 months to pay the entire amount.