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SIMPLE INTEREST

SOLVED EXAMPLES

Example 1 :
If the simple interest on Rs. 1500 increases by Rs. 30. When the time increases by ‘8’ years. Find the rate of interest per annum.
   (1) 0.5%       (2) 0.25%     (3) 0.75%     (4) 1.25%     (5) None of these
Sol. (2) Initially

 

Example 2 :
Rajiv took a loan at simple interest rate of 6% in the 1 year with an increase of 0.5% in each subsequent year. She paid interest of Rs. 3375 after 4 years. How much loan did she take.
   (1) 15800      (2) 12500    (3) 33250   (4) 15600    (5) None of these
Sol. (2) Total paid interest = 3375
              Rate = 6% and increasing by 0.5% every year.
              Let total taken amount = P

 

Example 3 :
Raju invested an amount Rs. 3000 at the simple interest rate 2 1/2 %of percent per annum and another amount at the simple interest rate 5% p.a. The total interest earned at the end of   year on the total amount invested scheme 3 1/2 % p.a. Find the total amount invested.
(1) 2000 (2) 4000 (3) 5000 (4) 3500   (5) None of these
Sol. (3)
     
   ⇒  15000 + 10x = 7x + 21000
  ⇒ 3x = 6000  ⇒ x = 2000
     Total x+ 3000 = 5000
Alternate Method :
   
     x1 and x2 are deposits
     ⇒ 3000 × 5 + 10 x2 = 21000 + 7x2
     ⇒  x2 = 2000
     Total = 3000 + x2
    3000 + 2000 = 5000

 

Example 4 :
Rs. 800 becomes Rs. 956 in 3 yrs at certain simple interest rate of interest. If the rate of interest is increased by 4. What amount will Rs. 800 become in 3 years.
  (1) 1020     (2) 1025     (3) 1052    (4) 1010   (5) None of these
Sol. (3) P = 800, A = 956
               SI = A – P = 956 – 800 = 156
               T = 3 Yrs
             
             New rate = 6.5 + 4 = 10.5%
           
            Amount = P + SI = 800 + 252 = 1052

 

Example 5 :
What annual payment will discharge a debt of Rs. 5600, due 5 years hence at  the rate of 6% simple interest.
    (1) 500       (2) 560     (3) 1000      (4) 750           (5) None of these
Sol. (3)

 

EXERCISE

1. Rakesh borrowed some money at the rate of 7% p.a. for the 1st 3 years, 9% p.a. for the next 6 years and 10% p.a. for the period beyond 9 years. If the total interest paid by him at the end of 15 years is Rs. 4050. How much money did he borrow.
A: 3000
Solution:
Let his deposit                 = 100
Interest for 1st 3 years    = 21
Interest for next 6 years = 54
Interest for last 6 years   = 60
                                           135
Total interest = 135
When interest ‘135’ deposit amount is Rs. 100.
Therefore when interest is 4050, deposited amount =

 

2. A certain sum is invested for certain time. It amounts to Rs. 60 at 6% per annum. But when invested 3% p.a. It amount to Rs. 30. Find the time.
A: Not possible
Solution:
Amount = P + SI :   Amount = P + SI
SI = 60 – P           :   SI = 30 – P

 

3. A sum was put at simple interest at a certain rate for 2 years. Had it been put at 5% higher rate, it would have fetched Rs. 125 more. Find the sum.
A: 1250
Solution:
    Let the sum = Rs. x
    Rate of interest = y%
     New rate of interest = (y + 5)%
    
        ⇒   10x = 12500
  ⇒   x = 1250
Alternate Method :

  Sum = Rs. 1250
  A = 125, T = 2, x = 5.

 

4. The simple interest on a sum of money will be Rs. 400 after 3 years. In the next 3 years, principal becomes 4 times. What will be the total interest at the end of the 6th year.
A: 2000
Solution:
    
    SI for next 3 years


    
     Total SI at the end of 6th year = 400 +1600 = 2000
Alternate Method :
Interest = (n + 1)x               n = 4, x = 400
               = (4 + 1)400
               = 5 × 400 = 2000.

5. Certain amount 10 times in 15 years. In how many years it become 28 times on simple interest?
A: 45 yrs
Solution:
   Let the S.I = A – P = 10 P – P = 9P
  
   R = 60%
   SI = 28P – P = 27 P

6. A sum of Rs. 2600 is lent out in 2 part in such a way that the interest on one part at 10% for 5 yrs is equal to that another part is 9% for 6 years the sum lent out at 10% is ?
A: 1350
Let the sum one part is Rs. ‘x’ at 10% in 5years
Another part is Rs. (2600 – x) at 9% in 6 years
From question

⇒ 50x = 2600 54
⇒ x = 1350

Alternate Method :
            2600
10%                        9%
5yr =50              6yr = 54
LCM of 50, 54 = 270
The ratio = 54 : 50

 

7. A certain sum of money amounted to Rs. 1020 at 9% in a time in which Rs. 720 amounted to Rs.880 at 4%. If the rate of interest is simple. Find the sum.
A: 680
Solution:

 

8. Rs. 7914 is divided into three parts in such away that the first part at 3% per annum after 8 years, the second part 4% per annum after ‘5’ years and third part at 6% per annum after ‘2’ years give amount find each part.
A: 2515, 2714, 2614
Solution:

9. Venu invested a sum of money at a certain rate of interest for a period of 4 years had he invested the same sum for a period of 6 years the total interest earned by him would have been fifty % more that the earlier interest amount. What was the ratio of interest percent per annum.
A: can’t be determined
Solution:

10. A certain sum of money at SI amounts to Rs.1012 in 2 1/2 % years and to Rs.1067.20 in 4 years. The rate of interest per annum is
A: 4%
Solution:

Posted Date : 10-02-2021

 

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