State true or false: If Rs. 6400 was lent to Feroz and Rashmi at 15% per annum each, for

3
1
2

years and 5 years respectively, then the difference in the simple interest paid by them is Rs. 150.

Question

State true or false: If Rs. 6400 was lent to Feroz and Rashmi at 15% per annum each, for

3
    1
    2

years and 5 years respectively, then the difference in the simple interest paid by them is Rs. 150.

Accepted Answer

It is given that Rs. 6400 was lent to Feroz and Rashmi at 15% per annum each, for 312 years and 5 years respectively.For Feroz, the data is as follows,Principal = Rs. 6400.Rate of Interest = 15% p.a.Time =

3
    1
    2

years or

7
    2

years.Now the formula for calculating the simple interest (I) is given as follows,

I=
    
     P×R×T
    
     100

, where P denotes the principal, R denotes the rate of interest and T denotes the time in years.So, substituting the values and simplifying,

I=
      
       6400×15×
        7
        2

100

=
      
       3200×15×7
      
       100

=
      
       336000
      
       100

=3360

So, the interest that Feroz has to pay is found to be Rs. 3360.Now, for Rashmi, the data is as follows,Principal = Rs. 6400Rate = 15% p.a.Time = 5 years.So, substituting the values and simplifying, we get the interest as,

I=
      
       6400×15×5
      
       100

=
      
       480000
      
       100

=4800

So, the interest that Rashmi has to pay is found to be Rs. 4800.Now, computing the difference between both the interests, i.e., for Feroz and Rashmi, we get,

4800−3360=1440
 So, the difference between the interests paid by Feroz and Rashmi is found to be Rs. 1440.Hence, the statement is false.Hence, the correct option is (2).

State true or false:

If Rs. 6400 was lent to Feroz and Rashmi at 15% per annum each, for $312$ years and 5 years respectively, then the difference in the simple interest paid by them is Rs. 150.

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State true or false: If Rs. 6400 was lent to Feroz and Rashmi at 15% per annum each, for 3 1 2 years and 5 years respectively, then the difference in the simple interest paid by them is Rs. 150.