UPSC Insta–DART (Daily Aptitude and Reasoning Test) 7 Oct 2024
Kartavya Desk Staff
Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too.We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.
Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).
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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? a) 22 : 21 b) 11 : 21 c) 21 : 22 d) 21 : 11 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
#### 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?
• a) 22 : 21
• b) 11 : 21
• c) 21 : 22
• d) 21 : 11
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 %
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
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 %
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
• 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? a) Rs. 34000 b) Rs. 37200 c) Rs. 36400 d) Rs. 33200 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.
#### 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?
• a) Rs. 34000
• b) Rs. 37200
• c) Rs. 36400
• d) Rs. 33200
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.
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.
• 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? a) Rs. 1800000 b) Rs. 4536527 c) Rs. 1850000 d) Rs. 3830000 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.
#### 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?
• a) Rs. 1800000
• b) Rs. 4536527
• c) Rs. 1850000
• d) Rs. 3830000
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.
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.
• 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. a) Rs. 91000 b) Rs. 92000 c) Rs. 93000 d) Rs. 91500 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.
#### 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.
• a) Rs. 91000
• b) Rs. 92000
• c) Rs. 93000
• d) Rs. 91500
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.
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.
• 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. a) 3000 b) 4087 c) 3087 d) 4000 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.
#### 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.
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.
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.
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