**Q1. Rs. 1,000 is invested at 5% per annum simple interest. If the interest is added to the principal after every 10 years, the amount will become Rs. 2,000 after **

(a) 15 years

(b) 18 years

(c) 20 years

(d) 50/3 years

**S1. Ans.(d)**

**Sol.** SI(10)=(1000×5×10)/100

=500

Now principal = 1500

500=(1500×S×T)/100

6 2/3=T

Total time =10+20/3

=50/3

**Q2. Rs. 6,000 becomes Rs. 7,200 in 4 years. If the rate becomes 1.5 times of itself, the amount of the same principal in 5 years will be **

(a) Rs. 8,000

(b) Rs. 8,250

(c) Rs. 9,250

(d) Rs. 9,000

**S2. Ans.(b)**

**Sol. ** 1200=(6000×R×4)/100

R=5%

New Rate =7.5%

S.I. =(6000×7.5×5)/100

= 2250

Amount = P + S.I.

= 8250

**Q3. With a given rate of simple interest, the ratio of principal and amount for a certain period of time is 4 : 5. After 3 years, with the same rate of interest, the ratio of the principal and amount becomes 5 : 7. The rate of interest is : **

(a) 4%

(b) 6%

(c) 5%

(d) 7%

**S3. Ans.(c)**

**Sol.** Principal/Amount=(4×5)/(5×5)=20/25

After three year =P/A=(5×4)/(7×4)=20/28

In three year S.I. = 28x-25x

=3x

3x=(20x×R×3)/100

R=5%

**Q4. A sum of money at some rate of simple interest amounts to Rs. 2900 in 8 years and to 3,000 in 10 years. The rate of interest per annum is **

(a) 4%

(b) 5/2%

(c) 3%

(d) 2%

**S4. Ans.(d)**

**Sol.** Let the Principal = P

(2900-P)=(P×r×8)/100 ………….(i)

(3000-P)=(P×r×10)/100 ………..(ii)

Divided (i) by (ii)

29000-10P=24000-8P

5000=2P

P=2500

400=(2500×8×r)/100

r=2%

**Q5. A sum of money lent at simple interest amounts to Rs. 880 in 2 years and to Rs. 920 in 3 years.Then the rate of interest: **

(a) 5

(b) 8

(c) 10

(d) 15

** S5. Ans.(a)**

**Sol.** S.I. for one year =920-880

= 40

S.I. for two year =80

P = 800 – 80

= 800

80=(800×r×2)/100

r=5%

**Q6. The simple interest on a sum of money is 1/9 of the principal and the number of years is equal to the rate of interest per annum. The rate per annum is : **

(a) 3%

(b) 1/3%

(c) 10/3%

(d) 3/10%

**S6. Ans.(c)**

**Sol.** P/9=(P×r×r)/100

r=10/3 %

**Q7. A man invests half of his capital at the rate of 10% per annum, one-third at 9% and the rest at 12% per annum. The average rate of interest per annum, which he gets is : **

(a) 9%

(b) 10%

(c) 10.5%

(d) 12%

**S7. Ans.(b)**

**Sol.** Let the total Principal = 6P

S.I. =(3P×10)/100+(2P×9)/100+(P×12)/100

=6P×10/100

Rate of Interest = 10%

**Q8. Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years ? **

(a) Rs. 1020.80

(b) Rs. 1025

(c) Rs. 1052

(d) Rs. 1050

**S8. Ans.(c)**

**Sol.** 156=(800×r×3)/100

r=6.5

Now r=6.5+4=10.5

S.I. =(800×10.5×3)/100

= 252

Final Amount = 800 + 252

= 1052

**Q9. If the amount is 2.25 times of the sum after 2 years at compound interest (compound annually), the rate of interest per annum is **:

(a) 25%

(b) 30%

(c) 45%

(d) 50%

** S9. Ans.(d)**

**Sol.** [1+r/100]^2=2.25

1+r/100=1.5

r/100=0.5

r=50%

**Q10. A sum borrowed under compound interest doubles itself in 10 years. When will it become fourfold of itself at the same rate of interest? **

(a) 15 years

(b) 20 years

(c) 24 years

(d) 40 years

**S10. Ans.(b)**

**Sol.**

Year Sum

10 2P

10 × 2 → (2)^2P=4P

Hence, required time= 20 years

**Q11. In what time will Rs. 1000 amounts to Rs. 1331 at 20% per annum, compounded half yearly ? **

(a) 3/2 years

(b) 2 years

(c) 1 years

(d) 2 1/2 years

**Q12. A sum of money invested at compound interest amounts to Rs. 650 at the end of first year and Rs. 676 at the end of second year. The sum of money is : **

(a) Rs. 600

(b) Rs. 540

(c) Rs. 625

(d) Rs. 560

**S12. Ans.(c)**

**Sol.** Interest on 650 for one year = 26

26=(650×r×1)/100

r=4%

650=P[1+4/100]

=625

**Q13. The principal, which will amount to Rs. 270.40 in 2 years at the rate of 4% per annum compound interest, is : **

(a) Rs. 200

(b) Rs. 225

(c) Rs. 250

(d) Rs. 220

**S13. Ans.(c)**

**Sol.** A.T.Q.

270.40=P×26/25×26/25

P=250

**Q14. The compound interest on a certain sum of money at a certain rate for 2 years is Rs. 40.80 and the simple interest on the same sum is Rs. 40 at the same rate and for the same time. The rate of interest is : **

(a) 2% per annum

(b) 3% per annum

(c) 4% per annum

(d) 5% per annum

**S14. Ans.(c)**

**Sol.** Interest for one year = 20

Interest on these 20 rupee =40.8-40

=0.8

0.8=(20×r×1)/100

r=4%

**Q15. The compound interest on a certain sum of money invested for 2 years at 5% per annum is Rs. 328. The simple interest on the sum, at the same rate and for the same period will be : **

(a) Rs. 320

(b) Rs. 308

(c) Rs. 300

(d) Rs. 287

**S15. Ans.(a)**

**Sol.** A.T.Q.

P×1.05×1.05=P+328

P[1.1025]=P+328

P×0.1025=328

P=328/0.1025=3200

S.I. =(3200×10)/100=320