## S.I and C.I Problem with Explanations

S.I and C.I is an important chapter. From Boat and Stream chapter at least 1-2 problems will appear on all competitive exams like SSC and bank exams (SBI and IBPS-clerk and PO). This section will teach you to understand S.I and C.I problems with explanation and short cut to solve problems quickly

**S.I & C.I – Study material for all competitive exams**

S.I and C.I is a part of quantitative or numerical aptitude section for all competitive exams. This chapter will give brief explanation to S.I and C.I Problems. This will be very helpful to crack all competitive exams with more marks. “Practice makes a man perfect” so please practice more problems with different models. All the best for your preparations and success.

### Simple Interest Important formula:

*Principal:*The money borrowed or lent out for a certain period is called the

*principal*or the*sum*.*Interest:*Extra money paid for using other’s money is called

*interest*.- Simple Interest (S.I.):
If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called

*simple interest*.Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then

a) Simple interest = (P * R * T/100)

b) P = (100 * S.I / R * T )

c) R = (100 * S.I / P * T )

d) T = (100 * S.I / P * R )

### Compound Interest Important formula:

### S.I & C.I Problem with Explanations

**1) What is the difference between Simple Interest and Compound Interest on Rs 70,000 ar 20% rare of interest in one and a half year if Compound Interest is compounded half yearly.**** A) Rs 2070**** B) Rs 2160**** C) Rs 2170**** D) Rs 2060**** E) None of these**

**Answer with Explanation:**

SI on 1 (1/2) year= 20*1.5=30%

SI on 1 (1/2) years of compounded half yearly make rate half yearly and time double

r=10%=1/10 ; t=3 years

10——11

10——11

10——11

1000—-1331

r=331/1000*100=33.1

33.1%of 70,000 = 2170

**2) Divide Rs 20,816 between A and B so that A’s share at the end of 7 years is equal to B’s share at the end of 9 years with compound interest being 4% p.a**** A) 10716, 10100**** B) 10616, 10200**** C) 10816, 10000**** D) 10800, 10016**** E) None of these**

**Answer with Explanation:**

second part + (4+4 +16/100) of second part = first part

second part + 8.16% of second part= first part

first part/second part= 108.16/100 = 10816/10000

**3) Find the simple interest and compound interest of Rs 15000 at 20% rate of interest after 3 years.**** A) 9000, 11000**** B) 8000, 11920**** C) 9000, 10920**** D) 6000, 9000**** E) None of these**

**Answer with Explanation:**

SI= 20*3=60%=9000

CI=

3000 ———— 3000 ———3000

——————-600————–600

————————————–600

————————————–120

=> 9000+1800+120=10920

**4) A man borrows Rs 8000 at 10% compounded rate of interest. At the end of each year he pays back Rs 2200. How much amount should he pay at the end of the third year to clear all his dues?**** A) Rs 5500**** B) Rs 5466**** C) Rs 5666**** D) Rs 5566**** E) None of these**

**Answer with Explanation:**

first year=8000+800=8800-2200=6600

second year=6600+660=7260-2200=5060

third year=5060+506=5566

**5) What sum of money at compound interest will amount to Rs 32000 in 3 years at the rate of interest 20% in first years, 16 (2/3)% in second year and 14 (2/7)% in third year.**** A) Rs 18,000**** B) Rs 20,000**** C) Rs 22,000**** D) Rs 25,000**** E) None of these**

**Answer with Explanation:**

1^{st} year = 20% =1/5————-5 ————-6

2^{nd} year = 16 (2/3)= 1/6——-6————–7

3^{rd} year = 14 (2/7) =1/7 ——-7————–8

———————————-= 210———336 on simplifying = 5:8

r=(8-5)/5*100=60%

160%=32000

100%=20000

**6) If the difference between Simple Interest and Compound Interest at 10% p.a rate of interest for 3 years is Rs. 930, then find the Sum.**** A) Rs 25,000**** B) Rs 30,000**** C) Rs 35,000**** D) Rs 40,000**** E) None of these**

**Answer with Explanation:**

On SI, Rate for 3 years=3*10=30%

On CI rate for 3 years – 10%=1/10

10—–11

10—–11

10—–11

1000—-1331

=1331-1000/1000 *100=33.1%

Difference=33.1-30=3.1%

3.1%=930

100%=Rs 30,000

**7) On a certain rate of interest a sum of Rs 5000 becomes Rs 16,200 in certain years at compound interest. In half of the time given, this sum will become?**** A) Rs 10,000**** B) Rs 5,600**** C) Rs 9,000**** D) Cannot be determined**** E) None of these**

**Answer with Explanation:**

a————————b—————c

5000—————– X ————16200

———–t——————- t ————

As we have to calculate the sum for half time, both time period is same, and hence

a:b = b:c

5000:x = x:16200

x=Rs 9000

**8) If a certain sum becomes double in 3 years at certain rate of interest at C.I. Then in how many years it will become 16 times?**** A)12 years**** B) 24 years**** C) 8 years**** D) Cannot be determined**** E) None of the above**

**Answer with Explanation:**

In C.I P increases like

P——-2P——–4P———8P——–16P

—-3yrs—–3yrs—–3yrs——-3yrs

total=3+3+3+3=12 years

**9) Ram invests two sum of money A and B at 10% p.a. and 20% p.a respectively at CI for 2 years. IF the total interest on both the sum is Rs 5350 then find the sum invested in A if the total sum of A and B was Rs 20,000?**** A) Rs 5,000**** B) Rs 10,000**** C) Rs 12,000**** D) Rs 15,000**** E) None of these**

**Answer with Explanation:**

At 10% CI in 2 years=21 %

At 20% Ci in 2 years =44%

and 5350 is 107/4% of 20000, by using allegation

A B

21 44

107/4

3 1

A=3/4*20000= Rs 15000

**10) The compound interest on a certain sum for 2 years at a certain rate of interest is Rs 1025 and Simple Interest on the same sum, same time and same rate of interest is Rs 1,000. Then find the C.I for same sum in 3 years.**** A) Rs 1575.25**** B) Rs 1576.25**** C) Rs 1576.75**** D) Rs 1575.75**** E) None of these**

**Answer with Explanation:**

SI for 2 years = Rs 1000 =.> Si 1 year = Rs 500

In the second years Rs 25 is added in CI (1025-1000) which is 5% of 500

Hence R=5%

5%=500

100%=10000

sum=10000

CI for 3 years= RS 1576.25