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Question 1 of 5
1. Question
Akarsh invests Rs. x in insurance which gives her returns at 21% annually and Rs. y in mutual funds which gives her returns of 10% compounded half yearly. If Akarsh gets the same returns from both the investments after 1 year, then what is the square root of the ratio of x to y?
Correct
Answer: Option (c)
Explanation
Amount earned from insurance after one year;
A1 = (100 + Interest) × Principal = 121% of x
Applying net% effect in the 2nd scenario to get th effective rate of interest compound half-yearly, we get
Net% effect = x + y + xy %
100
Here, a = b = 5%
= 5 + 5 + (5 × 5)/100 = 10.25%
∴ Amount earned from mutual funds
A2 = (100 + interest) × Principal = (100 + 10.25)% = 110.25% of y
Given, A1 = A2
121% of x = 110.25% of y
∴ x/y = 110.25/121 = 441/484
(x/y)1/2 = (441/484) 1/2 = 21 : 22 Hence, option C is correct
Incorrect
Answer: Option (c)
Explanation
Amount earned from insurance after one year;
A1 = (100 + Interest) × Principal = 121% of x
Applying net% effect in the 2nd scenario to get th effective rate of interest compound half-yearly, we get
Net% effect = x + y + xy %
100
Here, a = b = 5%
= 5 + 5 + (5 × 5)/100 = 10.25%
∴ Amount earned from mutual funds
A2 = (100 + interest) × Principal = (100 + 10.25)% = 110.25% of y
Given, A1 = A2
121% of x = 110.25% of y
∴ x/y = 110.25/121 = 441/484
(x/y)1/2 = (441/484) 1/2 = 21 : 22 Hence, option C is correct
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Question 2 of 5
2. Question
Ishwar borrows a sum of Rs. 64000 at 5% pa compound interest. He repays a certain amount at the end of one year and the balance amount of Rs. 35700 at the end of the second year. What amount does he repay in the first year?
Correct
Answer: Option (d)
Explanation
Sum = Rs. 64000
∴ CI for 1st year = (64000 × 5)/100= Rs 3200
∴ A = 64000 + 320 = Rs. 67200
let the amount repaid be Rs.
Then, the sum at the beginning of the 2nd year = 67200 – x
Amount at the 2nd year = {(100 + Interest) /100 } × Principal × time
⇒ 35700 = 1.05 × (67200 – x) × 1
⇒ x = Rs. 33200. Hence, option D is correct.
Incorrect
Answer: Option (d)
Explanation
Sum = Rs. 64000
∴ CI for 1st year = (64000 × 5)/100= Rs 3200
∴ A = 64000 + 320 = Rs. 67200
let the amount repaid be Rs.
Then, the sum at the beginning of the 2nd year = 67200 – x
Amount at the 2nd year = {(100 + Interest) /100 } × Principal × time
⇒ 35700 = 1.05 × (67200 – x) × 1
⇒ x = Rs. 33200. Hence, option D is correct.
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Question 3 of 5
3. Question
The income of a company increases 20% pa. If its income is Rs. 2664000 in the year 1998, what was its income in 1996?
Correct
Answer: Option (c)
Explanation
We can solve this question by the net% effect formula,
CI for 2 years at the rate of 20% pa,
= 20 + 20 + (20 × 20) / 100 = 44%
Let the sum be x,
Amount given = 2664000
So, (100 + 44)% of x = 2664000
x = (2664000 × 100) / 144 = 1850000 Hence, option C is correct.
Incorrect
Answer: Option (c)
Explanation
We can solve this question by the net% effect formula,
CI for 2 years at the rate of 20% pa,
= 20 + 20 + (20 × 20) / 100 = 44%
Let the sum be x,
Amount given = 2664000
So, (100 + 44)% of x = 2664000
x = (2664000 × 100) / 144 = 1850000 Hence, option C is correct.
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Question 4 of 5
4. Question
Ranjan invested a certain amount in scheme A, where the interest compounds annually. Simultaneously, he invested an equal amount in scheme B, which earns simple interest. The difference between the compound interest and simple interest earned over 3 years from both schemes, at a 10% rate of interest, totals Rs 2821. Determine the initial investment in scheme A.
Correct
Answer: Option (a)
Explanation
The correct answer is option 1 i.e. Rs. 91000
Rate = 10%, Let Principal = P
S.I. = (P × 10 × 3) /100 = 3P/10
C.I. = P{(1 + 1/10)3 – 1}
C.I. – S.I. = 2821
P{(1 + 1/10)3 – 1} – 3P/10 = 2821
P{(11/10)3 – 1 – 3/10} = 2821
P{(1331 – 1000 – 300) /1000} = 2821
P{31/1000} = 2821
P = Rs. 91,000 Hence, option A is correct.
Incorrect
Answer: Option (a)
Explanation
The correct answer is option 1 i.e. Rs. 91000
Rate = 10%, Let Principal = P
S.I. = (P × 10 × 3) /100 = 3P/10
C.I. = P{(1 + 1/10)3 – 1}
C.I. – S.I. = 2821
P{(1 + 1/10)3 – 1} – 3P/10 = 2821
P{(11/10)3 – 1 – 3/10} = 2821
P{(1331 – 1000 – 300) /1000} = 2821
P{31/1000} = 2821
P = Rs. 91,000 Hence, option A is correct.
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Question 5 of 5
5. Question
Rs. 5887 is divided between Shankar and Raju, such that Shankar’s share at the end of 9 years is equal to Raju’s share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shankar.
Correct
Answer: Option (c)
Explanation
Shyam’s share * (1+0.05)9 = Ram’s share * (1 + 0.05)11
Shyam’s share / Ram’s share = (1 + 0.05)11 / (1+ 0.05)9 =
(1+ 0.05)2 = 441/400
Therefore Shyam’s share = (441/841) * 5887 = 3087 Hence, option C is correct.
Incorrect
Answer: Option (c)
Explanation
Shyam’s share * (1+0.05)9 = Ram’s share * (1 + 0.05)11
Shyam’s share / Ram’s share = (1 + 0.05)11 / (1+ 0.05)9 =
(1+ 0.05)2 = 441/400
Therefore Shyam’s share = (441/841) * 5887 = 3087 Hence, option C is correct.
