# How much equal money should a person pay in 5 installments to discharge a debt of ₹ 1100 which got due in 5 years at 5% p.a. of simple interest?

## Answer

Correct Answer : c ) ₹ 200

Explanation :**Quick Approach**

Amount of money paid in each instalment = \({100P \over 100T+ {T(T-1)R \over 2}}\)

Where, P is the principal, T is the time period and R is the rate of interest

Thus,

Amount of money after after each year=\({100*1100 \over 100*5+ {5(5-1)*5 \over 2}}\)

⇒\({110000 \over 500+50}=₹200\)

Hence, (c) is the correct answer.

**Basic Approach**

Let us assume equal amount paid after each year be ₹ X

Now, in the first year due to the payment of ₹ X, the interest on ₹ X for 4 years will be saved

Similarly, for the second year due to the payment of ₹ X, the interest on ₹ X for 3 years will be saved

And, for the third year due to the payment of ₹ X, the interest on ₹ X for 2 years will be saved

And, for the fourth year due to the payment of ₹ X, the interest on ₹ X for 1 years will be saved

While for the payment of ₹ X done in final year no saving of interest will be done as all the money will be paid by that time.

Hence, we can say that ₹ 1100 which got due in 5 years represents the sum of money paid in equal instalment and the interest save d on those instalments.

We know that

\(SI={PRT \over 100}\)

Where, P is the principal, T is the time period and R is the rate of interest

Thus,

\(1100=(X+{X*4*5 \over 100})+(X+{X*3*5 \over 100})+(X+ {X*2*5 \over 100})+(X+{X*1*5 \over 100})+X\)

\(5X+{20X \over 100}+{15X \over 100}+{10X \over 100}+{5X \over 100}=1100\)

\({550X \over 100}=1100\)

X = ₹ 200

Hence, (c) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc.

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