UPSC Insta–DART (Daily Aptitude and Reasoning Test) 13 Sep 2024

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 Three Statements S1, S2 and S3 are given below followed by a Question: S1: Simple Interest accrued in two years on an amount P, at rate of interest R is Rs. 44,000. S2: The amount after some years on an amount P, at rate of interest R is Rs. 154000. S3: Difference between the C.I. and S.I. earned in two years on the amount P, and at rate of interest R is Rs. 120. Question: What is the rate of interest? a) S1 and S3 together are sufficient to answer the Question b) S2 alone is sufficient to answer the Question c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the question d) S1 and S2 together are sufficient to answer the Question Correct Answer: Option (a) Explanation: From S1: SI = PRT/100 Or 44000 = PR × 2/100 Or PR = 2200000 ………….(i) From S2: P + PRT/100 = 154000 From S3: Difference between the C.I. and S.I. = PR2/1002 = 120 From S1 and S3: PR2/1002 = 120 (PR × R)/1002 = 120 Putting the value of PR from equation (i), we get: (2200000 × R)/1002 = 120 Or R = 120 × 10000/2200000 = 12/22 = 6/11 Thus, by using S1 and S3, we can find the value of R. Hence, option (a) is the correct answer. Incorrect Answer: Option (a) Explanation: From S1: SI = PRT/100 Or 44000 = PR × 2/100 Or PR = 2200000 ………….(i) From S2: P + PRT/100 = 154000 From S3: Difference between the C.I. and S.I. = PR2/1002 = 120 From S1 and S3: PR2/1002 = 120 (PR × R)/1002 = 120 Putting the value of PR from equation (i), we get: (2200000 × R)/1002 = 120 Or R = 120 × 10000/2200000 = 12/22 = 6/11 Thus, by using S1 and S3, we can find the value of R. Hence, option (a) is the correct answer.

#### 1. Question

Three Statements S1, S2 and S3 are given below followed by a Question:

S1: Simple Interest accrued in two years on an amount P, at rate of interest R is Rs. 44,000.

S2: The amount after some years on an amount P, at rate of interest R is Rs. 154000.

S3: Difference between the C.I. and S.I. earned in two years on the amount P, and at rate of interest R is Rs. 120.

Question: What is the rate of interest?

• a) S1 and S3 together are sufficient to answer the Question

• b) S2 alone is sufficient to answer the Question

• c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the question

• d) S1 and S2 together are sufficient to answer the Question

Answer: Option (a)

Explanation:

SI = PRT/100

Or 44000 = PR × 2/100

Or PR = 2200000 ………….(i)

P + PRT/100 = 154000

Difference between the C.I. and S.I. = PR2/1002 = 120

From S1 and S3:

PR2/1002 = 120

(PR × R)/1002 = 120

Putting the value of PR from equation (i), we get:

(2200000 × R)/1002 = 120

Or R = 120 × 10000/2200000 = 12/22 = 6/11

Thus, by using S1 and S3, we can find the value of R.

Hence, option (a) is the correct answer.

Answer: Option (a)

Explanation:

SI = PRT/100

Or 44000 = PR × 2/100

Or PR = 2200000 ………….(i)

P + PRT/100 = 154000

Difference between the C.I. and S.I. = PR2/1002 = 120

From S1 and S3:

PR2/1002 = 120

(PR × R)/1002 = 120

Putting the value of PR from equation (i), we get:

(2200000 × R)/1002 = 120

Or R = 120 × 10000/2200000 = 12/22 = 6/11

Thus, by using S1 and S3, we can find the value of R.

Hence, option (a) is the correct answer.

• Question 2 of 5 2. Question Two statements S1 and S2 are given below followed by a question. S1: The interest after one year was Rs. 100 and the initial sum was Rs. 1000. S2: The difference between simple and compound interest on a sum of Rs. 100 at the end of two years was Rs. 10. Question: What was the compound interest after three years? a) S1 alone is sufficient to answer the Question b) S2 alone is sufficient to answer the Question c) Either S1 alone or S2 alone is sufficient to answer the Question d) Both S1 and S2 are required to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question Correct Answer: Option (c) Explanation: From S1: Principal (P) = Rs. 1000, Interest (I) = Rs. 100, Time (n) = 1 year For 1 year simple and compound interests are the same. Thus, we can find rate of interest by using, S.I. = Prn/100. Now, Compound Interest (CI) = P {(1 + (r/100)n} – P P, r and n are known, so CI can be calculated after three years. Hence, S1 alone is sufficient to answer the question. From S2: Difference between S.I. and C.I. = Rs. 10, P = Rs. 100, n = 2 years Difference between S.I. and C.I. for 2 years = P × (r/100)2 So, r can be calculated. Hence, CI after three years can be found. Therefore, statement 2 alone is sufficient to answer the question. Thus, either S1 alone or S2 alone is sufficient to answer the Question. Hence, option (c) is correct answer. Incorrect Answer: Option (c) Explanation: From S1: Principal (P) = Rs. 1000, Interest (I) = Rs. 100, Time (n) = 1 year For 1 year simple and compound interests are the same. Thus, we can find rate of interest by using, S.I. = Prn/100. Now, Compound Interest (CI) = P {(1 + (r/100)n} – P P, r and n are known, so CI can be calculated after three years. Hence, S1 alone is sufficient to answer the question. From S2: Difference between S.I. and C.I. = Rs. 10, P = Rs. 100, n = 2 years Difference between S.I. and C.I. for 2 years = P × (r/100)2 So, r can be calculated. Hence, CI after three years can be found. Therefore, statement 2 alone is sufficient to answer the question. Thus, either S1 alone or S2 alone is sufficient to answer the Question. Hence, option (c) is correct answer.

#### 2. Question

Two statements S1 and S2 are given below followed by a question.

S1: The interest after one year was Rs. 100 and the initial sum was Rs. 1000.

S2: The difference between simple and compound interest on a sum of Rs. 100 at the end of two years was Rs. 10.

Question: What was the compound interest after three years?

• a) S1 alone is sufficient to answer the Question

• b) S2 alone is sufficient to answer the Question

• c) Either S1 alone or S2 alone is sufficient to answer the Question

• d) Both S1 and S2 are required to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question

Answer: Option (c)

Explanation:

From S1:

Principal (P) = Rs. 1000, Interest (I) = Rs. 100, Time (n) = 1 year

For 1 year simple and compound interests are the same.

Thus, we can find rate of interest by using, S.I. = Prn/100.

Now, Compound Interest (CI) = P {(1 + (r/100)n} – P

P, r and n are known, so CI can be calculated after three years.

Hence, S1 alone is sufficient to answer the question.

From S2:

Difference between S.I. and C.I. = Rs. 10, P = Rs. 100, n = 2 years

Difference between S.I. and C.I. for 2 years = P × (r/100)2

So, r can be calculated.

Hence, CI after three years can be found.

Therefore, statement 2 alone is sufficient to answer the question.

Thus, either S1 alone or S2 alone is sufficient to answer the Question. Hence, option (c) is correct answer.

Answer: Option (c)

Explanation:

From S1:

Principal (P) = Rs. 1000, Interest (I) = Rs. 100, Time (n) = 1 year

For 1 year simple and compound interests are the same.

Thus, we can find rate of interest by using, S.I. = Prn/100.

Now, Compound Interest (CI) = P {(1 + (r/100)n} – P

P, r and n are known, so CI can be calculated after three years.

Hence, S1 alone is sufficient to answer the question.

From S2:

Difference between S.I. and C.I. = Rs. 10, P = Rs. 100, n = 2 years

Difference between S.I. and C.I. for 2 years = P × (r/100)2

So, r can be calculated.

Hence, CI after three years can be found.

Therefore, statement 2 alone is sufficient to answer the question.

Thus, either S1 alone or S2 alone is sufficient to answer the Question. Hence, option (c) is correct answer.

• Question 3 of 5 3. Question Sampath Gowda promised his younger sister Lakshmi Gowda, that he will give her pocket money every month, which will be equal to 50% of the compound interest on Rs. 390625 for two and half years at 4% per annum. How much pocket money will Lakshmi Gowda? a) Rs. 22,675 b) Rs. 20,070 c) Rs. 18,390 d) None of the above. Correct Answer: Option (d) Explanation: P = Rs. 390625, t = 2.5 years, r = 4% pa Now, C.I. = P[(1 + R/100)2 (1 + R/200) – 1] = 390625 {(1 + 4/100)2 (1 + 4/200) − 1} = 390625 [(26/25) × (26/25) × (51/50) − 1] = (390625×3226)/31250 = 125×3226/10 = Rs. 40325 Lakshmi Gowda will receive 50% of C.I. So, she will get (40325 × 50)/100 = Rs. 20162.50 Hence, option (d) is the correct answer. Incorrect Answer: Option (d) Explanation: P = Rs. 390625, t = 2.5 years, r = 4% pa Now, C.I. = P[(1 + R/100)2 (1 + R/200) – 1] = 390625 {(1 + 4/100)2 (1 + 4/200) − 1} = 390625 [(26/25) × (26/25) × (51/50) − 1] = (390625×3226)/31250 = 125×3226/10 = Rs. 40325 Lakshmi Gowda will receive 50% of C.I. So, she will get (40325 × 50)/100 = Rs. 20162.50 Hence, option (d) is the correct answer.

#### 3. Question

Sampath Gowda promised his younger sister Lakshmi Gowda, that he will give her pocket money every month, which will be equal to 50% of the compound interest on Rs. 390625 for two and half years at 4% per annum. How much pocket money will Lakshmi Gowda?

• a) Rs. 22,675

• b) Rs. 20,070

• c) Rs. 18,390

• d) None of the above.

Answer: Option (d)

Explanation:

P = Rs. 390625, t = 2.5 years, r = 4% pa

Now, C.I. = P[(1 + R/100)2 (1 + R/200) – 1]

= 390625 {(1 + 4/100)2 (1 + 4/200) − 1}

= 390625 [(26/25) × (26/25) × (51/50) − 1]

= (390625×3226)/31250

= 125×3226/10

= Rs. 40325

Lakshmi Gowda will receive 50% of C.I.

So, she will get (40325 × 50)/100 = Rs. 20162.50

Hence, option (d) is the correct answer.

Answer: Option (d)

Explanation:

P = Rs. 390625, t = 2.5 years, r = 4% pa

Now, C.I. = P[(1 + R/100)2 (1 + R/200) – 1]

= 390625 {(1 + 4/100)2 (1 + 4/200) − 1}

= 390625 [(26/25) × (26/25) × (51/50) − 1]

= (390625×3226)/31250

= 125×3226/10

= Rs. 40325

Lakshmi Gowda will receive 50% of C.I.

So, she will get (40325 × 50)/100 = Rs. 20162.50

Hence, option (d) is the correct answer.

• Question 4 of 5 4. Question Corporation Bank is offering a scheme wherein the amount at a certain rate of annual compound interest becomes three times of itself in 12 years. Under the same scheme, how long will an amount take to become twenty-seven times of itself ? a) 36 b) 24 c) 48 d) 32 Correct Answer: Option (a) Explanation: Amount = Principle [1 + (r/100)]n So, 3P = P [1 + (r/100)]12 or [1 + (r/100)]12 = 3 …………(i) According to the question, 27P = P {1 + (r/100)}n or 33 = {1 + (r/100)}n ………..(ii) On putting the value of 3 from equation (i) in equation (ii), we get: [{1 + (r/100)}12]3 = {1 + (r/100)}n or {1 + (r/100)}36 = {1 + (r/100)}n So, n = 36 Hence, option (a) is the correct answer. Incorrect Answer: Option (a) Explanation: Amount = Principle [1 + (r/100)]n So, 3P = P [1 + (r/100)]12 or [1 + (r/100)]12 = 3 …………(i) According to the question, 27P = P {1 + (r/100)}n or 33 = {1 + (r/100)}n ………..(ii) On putting the value of 3 from equation (i) in equation (ii), we get: [{1 + (r/100)}12]3 = {1 + (r/100)}n or {1 + (r/100)}36 = {1 + (r/100)}n So, n = 36 Hence, option (a) is the correct answer.

#### 4. Question

Corporation Bank is offering a scheme wherein the amount at a certain rate of annual compound interest becomes three times of itself in 12 years. Under the same scheme, how long will an amount take to become twenty-seven times of itself ?

Answer: Option (a)

Explanation:

Amount = Principle [1 + (r/100)]n

So, 3P = P [1 + (r/100)]12

or [1 + (r/100)]12 = 3 …………(i)

According to the question,

27P = P {1 + (r/100)}n

or 33 = {1 + (r/100)}n ………..(ii)

On putting the value of 3 from equation (i) in equation (ii), we get:

[{1 + (r/100)}12]3 = {1 + (r/100)}n

or {1 + (r/100)}36 = {1 + (r/100)}n

So, n = 36 Hence, option (a) is the correct answer.

Answer: Option (a)

Explanation:

Amount = Principle [1 + (r/100)]n

So, 3P = P [1 + (r/100)]12

or [1 + (r/100)]12 = 3 …………(i)

According to the question,

27P = P {1 + (r/100)}n

or 33 = {1 + (r/100)}n ………..(ii)

On putting the value of 3 from equation (i) in equation (ii), we get:

[{1 + (r/100)}12]3 = {1 + (r/100)}n

or {1 + (r/100)}36 = {1 + (r/100)}n

So, n = 36 Hence, option (a) is the correct answer.

• Question 5 of 5 5. Question Consider the following statements regarding the principles of Siddha medicine: Siddha medicine is based on the balance of five elements: earth, water, fire, air, and ether. Siddha treatments avoid the use of minerals and metals, focusing solely on herbal remedies. Siddha focuses on treating only physical ailments and does not include mental or spiritual aspects. Which of the statements given above are correct? a) 1 and 2 only b) 1 and 3 only c) 1 only d) 1, 2, and 3 Correct Solution: c) Statement 1 is correct as the Siddha system is based on balancing the five elements—earth, water, fire, air, and ether—within the body to maintain health and well-being. Statement 2 is incorrect because Siddha medicine does not avoid the use of minerals and metals; in fact, these substances play a crucial role in certain Siddha treatments alongside herbal remedies. Statement 3 is incorrect, as Siddha medicine adopts a holistic approach that includes physical, mental, and spiritual healing. Incorrect Solution: c) Statement 1 is correct as the Siddha system is based on balancing the five elements—earth, water, fire, air, and ether—within the body to maintain health and well-being. Statement 2 is incorrect because Siddha medicine does not avoid the use of minerals and metals; in fact, these substances play a crucial role in certain Siddha treatments alongside herbal remedies. Statement 3 is incorrect, as Siddha medicine adopts a holistic approach that includes physical, mental, and spiritual healing.

#### 5. Question

Consider the following statements regarding the principles of Siddha medicine:

• Siddha medicine is based on the balance of five elements: earth, water, fire, air, and ether.

• Siddha treatments avoid the use of minerals and metals, focusing solely on herbal remedies.

• Siddha focuses on treating only physical ailments and does not include mental or spiritual aspects.

Which of the statements given above are correct?

• a) 1 and 2 only

• b) 1 and 3 only

• d) 1, 2, and 3

Solution: c)

Statement 1 is correct as the Siddha system is based on balancing the five elements—earth, water, fire, air, and ether—within the body to maintain health and well-being.

Statement 2 is incorrect because Siddha medicine does not avoid the use of minerals and metals; in fact, these substances play a crucial role in certain Siddha treatments alongside herbal remedies.

Statement 3 is incorrect, as Siddha medicine adopts a holistic approach that includes physical, mental, and spiritual healing.

Solution: c)

Statement 1 is correct as the Siddha system is based on balancing the five elements—earth, water, fire, air, and ether—within the body to maintain health and well-being.

Statement 2 is incorrect because Siddha medicine does not avoid the use of minerals and metals; in fact, these substances play a crucial role in certain Siddha treatments alongside herbal remedies.

Statement 3 is incorrect, as Siddha medicine adopts a holistic approach that includes physical, mental, and spiritual healing.

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