**Q1. If the simple interest on a certain sum of money is 4/25 of the sum and the rate percent equals the number years, then the rate of interest per annum is:**

(a) 2%

(b) 3%

**(c) 4%**

(d) None of these

**Sol.**

**Let the principal be Rs. x**

**Then the simple interest (I)=4/25 x.**

**Let the rate of interest p.a. be r%, then time (T) = r years**

**∴ R=(100 × I)/(P × T)⇒r=(100 × 4/25 x)/(x × r)**

**⇒ r^2=400/25 or r=20/5=4%**

**Q2. If a certain sum of money borrowed at 5% per annum simple interest amounts to Rs. 1020 in 4 years, then the sum of money borrowed is:**

**(a) Rs. 850**

(b) Rs. 925

(c) Rs. 750

(d) None of these

**Sol.**

**We have, A = Rs. 1020**

**T = 4 years**

**R = 5% p.a.**

**Let the principal be Rs. x**

**Then interest (I) = A – P = 1020 – x**

**Therefore, by using formula,**

**P=(100 × I)/(R × T)**

**We have, x=(100×(1020 – x))/(5 × 4)**

**⇒ x = 5100 – 5x or 6x = 5100**

**Or, x=5100/6 = Rs. 850**

**∴ The sum of money borrowed = Rs. 850**

**Q3. If Rs. 1000 be invested at interest rate of 5% and the interest be added to the principal every 10 years, then the number of years in which it will amount to Rs. 2000 is:**

**(a) 16 2/3 years**

(b) 16 1/4 years

(c) 16 years

(d) None of these

**Sol.**

**The interest earned in 10 years on Rs. 1000 at 5% per annum**

**=(1000 × 5 × 10)/100 = Rs. 500**

**The principal now becomes = Rs. 1000 + Rs. 500 = Rs. 1500.**

**We now find the time in which Rs. 1500 becomes Rs. 2000 at 5% p.a.**

**P = Rs. 1500**

**A = Rs. 2000**

**I = A – P = 2000 – 1500 = Rs. 500, R = 5% p.a.**

**∴ Time (T) =(100 × I)/(R × P)=(100 × 500)/(5 × 1500)=6 2/3 years**

**∴ Total time =(10+6 2/3) years =16 2/3 years**

**Q4. Suresh lends Rs. 10000 for 2 years at 20% per annum simple interest. After 1 year, he receives Rs. 6000. How much will be he receive next year?**

(a) Rs. 5900

(b) Rs. 6400

**(c) Rs. 7200**

(d) None of these

**Sol.**

**Amount after 1 year = P(I+(R × T)/100)**

**=10000(1+(20 × 1)/100)**

**= Rs. 12000**

**After paying Rs. 6000, the remaining sum = Rs. 6000**

**∴ Amount obtained in the next year**

**=P(1+(R × T)/100)**

**= 6000 (1+(20 × 1)/100) = Rs. 7200**

**Q5. A sum of money doubles itself in 8 years. In how many years will it tripple?**

**(a) 16 years**

(b) 15 years

(c) 14 years

(d) None of these

**Sol.**

**We have, n = 2, T = 8 years, m = 3**

**∴ Required Time (T)=((m – 1)/(n – 1))×T**

**=((3 – 1)/(2 – 1))×8 = 16 years**

**Q6. A sum of Rs. 7700 is to be divided among three brothers Nikhil, Nitin and Nishant in such a way that simple interest on each part at 5% per annum after 1, 2 and 3 years, remains equal. The share of Nikhil is more than that of Nishant by:**

**(a) Rs. 2800**

(b) Rs. 2500

(c) Rs. 3000

(d) None of these

**Sol.**

**Hence T1=1,T2=2,T3=3**

**R1=R2=R3=5%**

**The shares of Nikhil, Nitin and Nishant will be in the ratio**

**1/(R1T1 )∶1/(R2T2 )∶1/(R3T3)=1/(1×5):1/(2×5)∶1/(3×5)**

**=1/1∶1/2∶1/3=6∶3∶2**

**Sum of proportionals = 6 + 3 + 2 = 11**

**∴ Share of Nikhil =6/11×7700 = Rs. 4200**

**Share of Nitin =3/11×7700 = Rs. 2100**

**Share of Nishant =2/11×7700 = Rs. 1400**

**Therefore, Nikhil’s share is 4200 – 1400 = Rs. 2800 more than that of Nishant.**

**Q7. Mr Sharma invested an amount of Rs. 12000 at a simple interest rate of 10% per annum and another amount at a simple interest rate of 20% per annum. The total interest earned at the end of one year on the total amount invested became 14% per annum. Find the total amount invested.**

**(a) Rs. 20000**

(b) Rs. 20800

(c) Rs. 21000

(d) None of these

**Sol.**

**Here P1 = Rs. 12000, R1 = 10%, P2 = ?, R2=20%, R = 14%**

**Therefore, using the formula**

**R=(P1 R1+ P2 R2)/(P1+ P2 )**

**We get 14=(12000 × 10 + P2 × 20)/(12000 + P2 )**

**Or, P2= Rs. 8000**

**∴ Total amount invested = Rs.(12000+8000) = Rs. 20000.**

**Q8. Vrinda borrowed Rs. 1000 to build a hut. She pays 5% simple interest. She lets the hut to Ram and receives a rent of Rs. 12 1/2 per month from Ram. In how many years Vrinda would clear off the debt?**

**(a) 10 years**

(b) 10 1/4 years

(c) 10 1/2 years

(d) None of these

**Sol.**

**Simple interest paid by Vrinda on Rs. 1000 for 1 year =(1000 × 5 × 1)/100 = Rs. 50**

**Rent received by Vrinda from Ram in 1 year**

**=12 1/2×12 = Rs. 150**

**∴ Net savings = Rs. 100**

**Thus, Vrinda will clear the debt of Rs. 1000 in 10 years**

**Q9. Manisha borrowed a sum of Rs. 1150 from Ajit at the simple rate of 6 per cent p.a. for 3 years. He then added some more money to the borrowed sum and lent it to Sunita for the same time at 9 per cent p.a. at simple interest. If Manisha gains Rs. 274.95 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Sunita?**

(a) Rs. 1290

**(b) Rs. 1785**

(c) Rs. 1285

(d) Rs. 1200

**Sol.**

**Suppose Manisha added Rs. x to the borrowed money**

**Then,**

**3 × (9 – 6)% of 1150 + (9 × 3)% of x = 274.95**

**⇒ 9% of 1150 + 27% of x = 274.95**

**⇒ x=(274.95 – 103.5)/27×100 = Rs. 635**

**∴ Required value = 635 + 1150 = Rs. 1785**

**Q10. The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate per cent per annum. The rate per annum is:**

(a) 5%

**(b) 6 2/3%**

(c) 6%

(d) 7 1/5%

**Sol.**

**Let the sum of money be P**

**I=(P×R×T)/100⇒4/9 P=(P×R×T)/100**

**∴R=√(400/9)=20/3=6 2/3%**