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A man starts repaying a loan as first installment of Rs. 100. If he increases the installments by Rs. 5 every month, what amount he will pay in 30 installments?

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Rs.240

Rs.245

Rs.250

Rs.300

answer is B.

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Detailed Solution

Given that,
A man starts repaying a loan as first installment of Rs. 100 and increases the installments by Rs. 5 every month.
Now, if a man pays Rs. 100 in first installment, so

a_{1} = 100 .

Now, he pays Rs. 100+5 in the second installment, so,

a_{2} = 105 .

Similarly,
He pays Rs. 105+5 in the third installment, so

a_{3} = 110 .

So, the series formed is 100, 105, 110, 115,..... which is in A.P.
We know the formula of

n^{th}

term,
The common difference will be,

d = a 2 − a 1 ⇒ d = 105 − 100 ⇒ d = 5

Similarly,

d = a_{3} - a_{2}

\Rightarrow d = 110 - 105

\Rightarrow d = 5

Since, the common difference is same, therefore, the given series is an A.P.
Now, we know,

t n = a + n − 1 d

Where,
The first term is a.
The common difference is d.
The number of terms are n.
Substitute 100 for a, 5 for d and 30 for n in the equation

t n = a + n − 1 d

to find the

30 t h

term.
Therefore,

t n = a + n − 1 d ⇒ t n = 100 + 30 − 1 × 5 ⇒ t n = 100 + 145 ⇒ t n = 245

Therefore, the amount he will pay in 30 installments is Rs 245.
Therefore, option 2 is correct.

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