Question

Jaspal Singh repays his total loan of Rs. $118000$ by paying every month starting with the first installment of Rs. $1000$. If he increases the installment by Rs. $100$ every month, what amount will be paid by him in the ${30}^{th}$ installment ? What amount of loan does he still have to pay after the ${30}^{th}$ installment ?

• A. Rs. $35000$
• B. Rs. $44500$
• C. Rs. $43420$
• D. Rs. $32450$

Answer 1

The correct option is B Rs. $44500$

Jaspal singh takes total loan $=Rs.118000$

Monthly instalments paid by Jaspal are $Rs.1000,Rs.1100,Rs.1200,\dots .$ Which form an AP with:

First term, $a=1000$

Common difference, d = 100

30^th term of this AP, $a_{30}=1000+(30-1)100$ [Using \ a_n = a + (n−1)d]

$=1000+29\times 100$

$=1000+2900=3900$

So, Rs. 3900 will be paid by Jaspal in the 30^th installment.

Now, Total amount paid in 30 installments is $=1000+1100+1200+.....+3900$

Here, First term, $a=1000,$

Last term, $l=3900$

And, number of terms, $n=30$

Therefore sum of 30 installments is given as,

$S_{30}=\frac{30}{2}[1000+3900]$

$=15(1000+3900)$

$=15\times 4900=73500$

Total amount that Jaspal still have to pay after the 30^th installment

= (Amount of loan) – (Sum of 30 installments)

$=118000–73500=Rs.44500$