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Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is? Answer is given as 20920.Please explain the answer.(CAT2019)?
Most Upvoted Answer
Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 1000...
Solution:
Let us calculate the interest earned by Amal and Bimal separately.
Interest earned by Amal:
Amount invested by Amal at 8% interest = Rs 12000
Amount invested by Amal at 6% interest compounded semi-annually = Rs 10000
Interest earned on the first investment = P(1 + R/100)ᵀ - P
Where P is the principal amount, R is the rate of interest and T is the time period.
Interest earned on the first investment = 12000(1 + 8/100)¹ - 12000 = Rs 960
Interest earned on the second investment = P(1 + R/2/100)²T - P
Interest earned on the second investment = 10000(1 + 6/2/100)² - 10000 = Rs 615.51
Total interest earned by Amal = Rs 960 + Rs 615.51 = Rs 1575.51
Interest earned by Bimal:
Amount invested by Bimal = Let it be X
Rate of interest = 7.5%
Time period = 1 year
Interest earned by Bimal = PRT/100
Interest earned by Bimal = X × 7.5 × 1/100 = 0.075X
We know that Amal and Bimal get the same amount of interest. Therefore,
0.075X = 1575.51
X = 1575.51/0.075
X = 21006.80
Therefore, the amount invested by Bimal is Rs 21006.80, which when rounded off to the nearest rupee is Rs 20920.
Let us calculate the interest earned by Amal and Bimal separately.
Interest earned by Amal:
Amount invested by Amal at 8% interest = Rs 12000
Amount invested by Amal at 6% interest compounded semi-annually = Rs 10000
Interest earned on the first investment = P(1 + R/100)ᵀ - P
Where P is the principal amount, R is the rate of interest and T is the time period.
Interest earned on the first investment = 12000(1 + 8/100)¹ - 12000 = Rs 960
Interest earned on the second investment = P(1 + R/2/100)²T - P
Interest earned on the second investment = 10000(1 + 6/2/100)² - 10000 = Rs 615.51
Total interest earned by Amal = Rs 960 + Rs 615.51 = Rs 1575.51
Interest earned by Bimal:
Amount invested by Bimal = Let it be X
Rate of interest = 7.5%
Time period = 1 year
Interest earned by Bimal = PRT/100
Interest earned by Bimal = X × 7.5 × 1/100 = 0.075X
We know that Amal and Bimal get the same amount of interest. Therefore,
0.075X = 1575.51
X = 1575.51/0.075
X = 21006.80
Therefore, the amount invested by Bimal is Rs 21006.80, which when rounded off to the nearest rupee is Rs 20920.
Community Answer
Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 1000...
P1(Principal)=12000 R1(Rate)=8% T(Time)=1 C.I annually
C.I(Compound intrest)=A(Amount)-P(Principal)
A=P(1+R/100)T
=12000*(1+ 8/100)1
=12000* 108/100
=12960
intrest= 12960-12000
= 960
P2=10000 R2=6% T=1 C.I semi annually
Amount(A2)= P*(1+R/200)2N
= 10000*(200+6/200)2
= 10000*206/200 *206/200
= 10609
C.I.2= A2-P2
= 10609-10000
= 609
Total Interest= C.I.1+C.I.2
= 960+609
=1569
S.I(Simple intrest)= Total intrest= 1569
R-7.5% T-1
1569= P*R*T/100
1569 = P*7.5*1/100
1569*100/7.5= P
20920= P
C.I(Compound intrest)=A(Amount)-P(Principal)
A=P(1+R/100)T
=12000*(1+ 8/100)1
=12000* 108/100
=12960
intrest= 12960-12000
= 960
P2=10000 R2=6% T=1 C.I semi annually
Amount(A2)= P*(1+R/200)2N
= 10000*(200+6/200)2
= 10000*206/200 *206/200
= 10609
C.I.2= A2-P2
= 10609-10000
= 609
Total Interest= C.I.1+C.I.2
= 960+609
=1569
S.I(Simple intrest)= Total intrest= 1569
R-7.5% T-1
1569= P*R*T/100
1569 = P*7.5*1/100
1569*100/7.5= P
20920= P
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Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is? Answer is given as 20920.Please explain the answer.(CAT2019)?
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Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is? Answer is given as 20920.Please explain the answer.(CAT2019)? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is? Answer is given as 20920.Please explain the answer.(CAT2019)? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is? Answer is given as 20920.Please explain the answer.(CAT2019)?.
Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is? Answer is given as 20920.Please explain the answer.(CAT2019)? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is? Answer is given as 20920.Please explain the answer.(CAT2019)? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is? Answer is given as 20920.Please explain the answer.(CAT2019)?.
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