| A sum of Rs. 6240 is paid off in 30 installments in such a way that each installment is Rs. 10 more than the preceding installment. What is the value of the first installment? [NICL (AO) 2014] |
A) Rs. 30
B) Rs. 45
C) Rs. 63
D) Rs. 72
E) Rs. 57
Correct Answer: C
Solution :
| Here, \[\text{sum}=6240={{S}_{n}},\]d = 10, |
| a = first installment = ?, n = 30 |
| Here, it is an arithmetic progression. |
| \[\because \] \[{{S}_{n}}=\frac{n}{2}\,\,[2a+(n-1)\,d]\] |
| \[\therefore \] \[6240=\frac{30}{2}[2\times a+(30-1)\times 10]\] |
| \[\Rightarrow \] \[6240=15\,(2a+290)\]\[\Rightarrow \]\[416=2a+290\] |
| \[\Rightarrow \] \[2a=416-290\]\[\Rightarrow \]\[2a=126\] |
| \[\Rightarrow \] \[a=63\] |
| Hence, first installment = Rs. 63 |
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