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A sum of Rs.7140 is to be divided between Anita and Bala who are respectively 18 and 19 yr old, in such a way that if their shares will be invested at 4% per annum at compound interest, they will receive equal amounts on attaining the age of 21 year. The present share of Anita is
- a)4225
- b)4352
- c)3500
- d)4000
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A sum of Rs.7140 is to be divided between Anita and Bala who are respe...
Amount got by Anita after 3 yr = Amount got by Bala after 2 yr
x*(26/25)³ = (7140 – x)*(26/25)
26/25 = 7140 – x / x
x = 3500
x*(26/25)³ = (7140 – x)*(26/25)
26/25 = 7140 – x / x
x = 3500
Most Upvoted Answer
A sum of Rs.7140 is to be divided between Anita and Bala who are respe...
To solve this question, let's assume that Anita's share is x and Bala's share is Rs. 7140 - x.
Now, we need to find the value of x.
We are given that if their shares are invested at 4% per annum at compound interest, they will receive equal amounts on attaining the age of 21 years.
Using the compound interest formula:
A = P(1 + r/n)^(nt)
A = Final amount
P = Principal amount
r = Rate of interest
n = Number of times interest is compounded per year
t = Number of years
Since both Anita and Bala will receive equal amounts, we can set up the equation:
x(1 + 0.04/1)^(1*(21-18)) = (7140 - x)(1 + 0.04/1)^(1*(21-19))
Simplifying this equation:
x(1.04)^3 = (7140 - x)(1.04)^2
x(1.04)^3 = (7140 - x)(1.04)^2
x(1.124864) = (7140 - x)(1.0816)
1.124864x = 7140.5184 - 1.0816x
2.206464x = 7140.5184
x = 3234.40
Therefore, Anita's share is Rs. 3234.40.
To find Bala's share, we can subtract Anita's share from the total amount:
Bala's share = 7140 - 3234.40 = Rs. 3905.60
Since none of the given options match the calculated values, it appears that there is an error in the options provided. The correct answer cannot be determined from the given options.
Therefore, the correct answer is "None of these."
Now, we need to find the value of x.
We are given that if their shares are invested at 4% per annum at compound interest, they will receive equal amounts on attaining the age of 21 years.
Using the compound interest formula:
A = P(1 + r/n)^(nt)
A = Final amount
P = Principal amount
r = Rate of interest
n = Number of times interest is compounded per year
t = Number of years
Since both Anita and Bala will receive equal amounts, we can set up the equation:
x(1 + 0.04/1)^(1*(21-18)) = (7140 - x)(1 + 0.04/1)^(1*(21-19))
Simplifying this equation:
x(1.04)^3 = (7140 - x)(1.04)^2
x(1.04)^3 = (7140 - x)(1.04)^2
x(1.124864) = (7140 - x)(1.0816)
1.124864x = 7140.5184 - 1.0816x
2.206464x = 7140.5184
x = 3234.40
Therefore, Anita's share is Rs. 3234.40.
To find Bala's share, we can subtract Anita's share from the total amount:
Bala's share = 7140 - 3234.40 = Rs. 3905.60
Since none of the given options match the calculated values, it appears that there is an error in the options provided. The correct answer cannot be determined from the given options.
Therefore, the correct answer is "None of these."
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Community Answer
A sum of Rs.7140 is to be divided between Anita and Bala who are respe...
Amount got by Anita after 3 yr = Amount got by Bala after 2 yr
x*(26/25)³ = (7140 – x)*(26/25)
26/25 = 7140 – x / x
x = 3500
x*(26/25)³ = (7140 – x)*(26/25)
26/25 = 7140 – x / x
x = 3500
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A sum of Rs.7140 is to be divided between Anita and Bala who are respectively 18 and 19 yr old, in such a way that if their shares will be invested at 4% per annum at compound interest, they will receive equal amounts on attaining the age of 21 year. The present share of Anita isa)4225b)4352c)3500d)4000e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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