A and B went to a moneylender to borrow a total of 60,000rs.The money lender gave A a loan at 28%p.a and B a loan at a higher rate of interest.If both A and B had to pay the money lender 9,800rs as interest after a year,how much money was lent to B and at what rate of simple interest?
♤Please do with full explanation.
Answers
Answer:
25000,39.2%.
Step-by-step explanation:
In the question, we are given total principal of A and B as ₹60,000. So, first we will find Principal for A then money lent to B or principal for B and after that with principal of B we can easily calculate the rate of interest for B.
Let,
- The Principal for A = x.
- The Principal for B = 60000 - x.
Calculating Principal for A
Rate = 28% p.a.
Simple Interest = ₹9,800.
Time = 1year.
By Principal formula,
P = (100 × I)/(R × T)
=> x = (100 × 9800)/(28 × 1)
=> x = 980000/28
=> x = 35000.
∴ Principal for A = x = ₹35,000.
∴ Money lent to A is ₹35,000.
Calculating Principal for B
We have assumed before principal for B as
60000 - x.Now we are knowing the value of x, so let's put the value of x to get principal for B.
Principal = 60000 - x
=> Principal = 60000 - 35000
=> Principal = 25000.
∴ Money lent to B is ₹25,000.
Calculating Rate of Interest for B
Principal = ₹25,000.
Simple Interest = ₹9,800.
Time = 1year.
By Rate formula,
R = (100 × I)/(P × T)
=> R = (100 × 9800)/(25000 × 1)
=> R = 980000/25000
=> R = 980/25
=> R = 39.2.
∴ Rate of Interest for B is 39.2%.
Verification
For 1st answer
A + B = 60000
=> 35000 + 25000 = 60000
Hence, verified.
For second answer
In the question, it is given that the money lender gave A a loan at 28%p.a and B a loan at a higher rate of interest.
We got the rate of interest greater than A. So, our answer is correct.
B > A
39.2 > 28.
Hence, verified.
Used Abbreviations
P = Principal.
R = Rate of Interest.
I = Simple Interest.
T = Time.
________________________________