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

Solution:

Given, Jaspal Singh repays his total loan of Rs. 118000.

Monthly instalment is Rs. 1000.

We have to find the amount of loan he still have to pay after the 30th instalment, if he increases the instalment by Rs.100

Here, first term, a = 1000

Common difference, d = 100

To find a₃₀,

The nth term of the series in AP is given by

a_n = a + (n - 1)d

So, a₃₀ = 1000 + (30 - 1)(100)

= 1000 + 29(100)

= 1000 + 2900

a₃₀ = 3900

So, the amount paid by Jaspal Singh in 30 instalments = Rs.3900

Loan amount paid in 30 instalments = S₃₀

The sum of the first n terms of an AP is given by

S_n = n/2[2a + (n - 1)d]

So, S₃₀ = 30/2[2(1000) + (30 - 1)(100)]

= 15[2000 + 2900]

= 15(4900)

S₃₀= Rs.73500

Amount of loan to be paid after 30 instalments = (total loan) - (loan amount paid for 30 instalments)

= 118000 - 73500

= Rs.44500

Therefore, the amount of loan to be paid by Jaspal Singh after 30 instalments is Rs. 44500.

✦ Try This: Jaswanth repays his total loan of Rs 82000 by paying every month starting with the first instalment of Rs 800. If he increases the instalment by Rs 150 every month, what amount will be paid by him in the 10th instalment? What amount of loan does he still have to pay after the 10th instalment

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.4 Problem 9

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

Summary:

Jaspal Singh repays his total loan of Rs 118000 by paying every month starting with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month, the amount paid by him in the 30th instalment will be Rs.3900. The amount of loan he still has to pay after the 30th instalment is Rs.44500

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