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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 30th installment ? What amount of loan does he still have to pay after the 30th installment ?

A
Rs. 35000
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B
Rs. 44500
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C
Rs. 43420
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D
Rs. 32450
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Solution

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,. Which form an AP with:

First term, a=1000

Common difference, d = 100

30th term of this AP, a30=1000+(301)100 [Using \ an = a + (n−1)d]

=1000+29×100

=1000+2900=3900

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

S30=302[1000+3900]

=15(1000+3900)

=15×4900=73500

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

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

=11800073500=Rs.44500


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