UPSC Insta–DART (Daily Aptitude and Reasoning Test) 24 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 Amar can do a piece of work in 20 days. Sanjay is 25% more efficient than Amar. Find the number of days it takes Sanjay to do the same piece of work. a) 14 days b) 16 days c) 12 days d) 18 days Correct Answer: Option (b) Explanation: Let the efficiency of Amar = x = 100%. Then, the efficiency of Sanjay = y = 125%. Ratio of efficiencies, x/y = 100%/125% = 4/5. As the time taken to complete a work is inversely proportional to the respective efficiencies, so the time taken by Amar (let, m) and Sanjay (let, n) to complete the work will be in the ratio of 5:4. So, m/n = 5/4 ⇒ 20/n = 5/4 ⇒ n = 16 days Incorrect Answer: Option (b) Explanation: Let the efficiency of Amar = x = 100%. Then, the efficiency of Sanjay = y = 125%. Ratio of efficiencies, x/y = 100%/125% = 4/5. As the time taken to complete a work is inversely proportional to the respective efficiencies, so the time taken by Amar (let, m) and Sanjay (let, n) to complete the work will be in the ratio of 5:4. So, m/n = 5/4 ⇒ 20/n = 5/4 ⇒ n = 16 days

#### 1. Question

Amar can do a piece of work in 20 days. Sanjay is 25% more efficient than Amar. Find the number of days it takes Sanjay to do the same piece of work.

• a) 14 days

• b) 16 days

• c) 12 days

• d) 18 days

Answer: Option (b)

Explanation:

Let the efficiency of Amar = x = 100%.

Then, the efficiency of Sanjay = y = 125%.

Ratio of efficiencies, x/y = 100%/125% = 4/5.

As the time taken to complete a work is inversely proportional to the respective efficiencies, so the time taken by Amar (let, m) and Sanjay (let, n) to complete the work will be in the ratio of 5:4.

So, m/n = 5/4

⇒ 20/n = 5/4

⇒ n = 16 days

Answer: Option (b)

Explanation:

Let the efficiency of Amar = x = 100%.

Then, the efficiency of Sanjay = y = 125%.

Ratio of efficiencies, x/y = 100%/125% = 4/5.

As the time taken to complete a work is inversely proportional to the respective efficiencies, so the time taken by Amar (let, m) and Sanjay (let, n) to complete the work will be in the ratio of 5:4.

So, m/n = 5/4

⇒ 20/n = 5/4

⇒ n = 16 days

• Question 2 of 5 2. Question Pulakeshi can do 1/2 of a work in 8 days. Harsha can do 25% of the same work in 5 days. Ashoka can do 1/4 of the same work in 4 days and Narasimha can do the same work in 12 days. Consider the following statements – Harsha works faster than Narasimha. Narasimha completes the work the fastest. Pulakeshi and Ashoka will complete the work in same time. Ashoka works faster than Harsha. Which of the given statements is/are correct? a) Only 1 b) Only 1 and 2 c) Only 2 and 3 d) 2, 3 and 4 Correct Ansewer: Option (d) Explanation: Pulakeshi can do 1/2 of a work in 8 days, it means he can do the whole work in (2 × 8) i.e. 16 days. Harsha can do 25% of the same work in 5 days, it means he can do the whole work in (4 × 5) i.e. 20 days. Ashoka can do 1/4 of the same work in 4 days, it means he can do the whole work in (4 × 4) i.e. 16 days. Narasimha can do the same work in 12 days. Here, we can see that Pulakeshi and Ashoka will complete the work in same time and Narasimha completes the work the fastest and Ashoka works faster than Harsha. Hence, statements 2, 3 and 4 are correct. Hence option (d) is correct. Incorrect Ansewer: Option (d) Explanation: Pulakeshi can do 1/2 of a work in 8 days, it means he can do the whole work in (2 × 8) i.e. 16 days. Harsha can do 25% of the same work in 5 days, it means he can do the whole work in (4 × 5) i.e. 20 days. Ashoka can do 1/4 of the same work in 4 days, it means he can do the whole work in (4 × 4) i.e. 16 days. Narasimha can do the same work in 12 days. Here, we can see that Pulakeshi and Ashoka will complete the work in same time and Narasimha completes the work the fastest and Ashoka works faster than Harsha. Hence, statements 2, 3 and 4 are correct. Hence option (d) is correct.

#### 2. Question

Pulakeshi can do 1/2 of a work in 8 days. Harsha can do 25% of the same work in 5 days. Ashoka can do 1/4 of the same work in 4 days and Narasimha can do the same work in 12 days.

Consider the following statements –

• Harsha works faster than Narasimha.

• Narasimha completes the work the fastest.

• Pulakeshi and Ashoka will complete the work in same time.

• Ashoka works faster than Harsha.

Which of the given statements is/are correct?

• b) Only 1 and 2

• c) Only 2 and 3

• d) 2, 3 and 4

Ansewer: Option (d)

Explanation:

Pulakeshi can do 1/2 of a work in 8 days, it means he can do the whole work in (2 × 8) i.e. 16 days.

Harsha can do 25% of the same work in 5 days, it means he can do the whole work in (4 × 5) i.e. 20 days.

Ashoka can do 1/4 of the same work in 4 days, it means he can do the whole work in (4 × 4) i.e. 16 days.

Narasimha can do the same work in 12 days.

Here, we can see that Pulakeshi and Ashoka will complete the work in same time and Narasimha completes the work the fastest and Ashoka works faster than Harsha. Hence, statements 2, 3 and 4 are correct. Hence option (d) is correct.

Ansewer: Option (d)

Explanation:

Pulakeshi can do 1/2 of a work in 8 days, it means he can do the whole work in (2 × 8) i.e. 16 days.

Harsha can do 25% of the same work in 5 days, it means he can do the whole work in (4 × 5) i.e. 20 days.

Ashoka can do 1/4 of the same work in 4 days, it means he can do the whole work in (4 × 4) i.e. 16 days.

Narasimha can do the same work in 12 days.

• Question 3 of 5 3. Question A group of workers can do a piece of job in 24 days. However, as 7 of them were absent, it took 6 more days for the rest of them to complete the job by working at an efficiency of 150%. How many people actually worked on the job to complete it? a) 15 b) 8 c) 7 d) 22 Correct Answer: Option (b) Explanation: Total amount of work = (no of people) × (no of days) × (hours) × (efficiency) Now, let there are x people initially Therefore, x × 24 × 100% = (x-7) × 30 × 150% Solving , we get x = 15 However, as 7 of them were absent (given) Hence, actually 8 people worked on the job. Incorrect Answer: Option (b) Explanation: Total amount of work = (no of people) × (no of days) × (hours) × (efficiency) Now, let there are x people initially Therefore, x × 24 × 100% = (x-7) × 30 × 150% Solving , we get x = 15 However, as 7 of them were absent (given) Hence, actually 8 people worked on the job.

#### 3. Question

A group of workers can do a piece of job in 24 days. However, as 7 of them were absent, it took 6 more days for the rest of them to complete the job by working at an efficiency of 150%. How many people actually worked on the job to complete it?

Answer: Option (b)

Explanation:

Total amount of work = (no of people) × (no of days) × (hours) × (efficiency)

Now, let there are x people initially

Therefore, x × 24 × 100% = (x-7) × 30 × 150%

Solving , we get x = 15

However, as 7 of them were absent (given)

Hence, actually 8 people worked on the job.

Answer: Option (b)

Explanation:

Total amount of work = (no of people) × (no of days) × (hours) × (efficiency)

Now, let there are x people initially

Therefore, x × 24 × 100% = (x-7) × 30 × 150%

Solving , we get x = 15

However, as 7 of them were absent (given)

Hence, actually 8 people worked on the job.

• Question 4 of 5 4. Question A is twice as good as workman as B so he can do a work in 40 days less than B. If they work together. In how many days they cal do the work? a) 80/4 days b) 80/5 days c) 80/3 days d) 80/6 days Correct Answer: Option (c) Explanation: A is twice as good as workman as B so he will take less time to do a piece of work than B and the ratio of time taken by A and B would be = 1 : 2 So, if there is a difference of one day (2–1), B takes 2 days As per question the difference in time taken by A and B is 40 days So, if the difference is of 40 days, B will take 2 × 40 = 80 days A takes 40 days less than B. So, A will take 40 days (80 – 40) to do the work. A’s one day work = 1/40 B’s one day work = 1/80 (A + B)’s one day work = (1/40) + ( 1/80) = 120/3200 = 3/80 So, working together will do the work in 80/3 days Incorrect Answer: Option (c) Explanation: A is twice as good as workman as B so he will take less time to do a piece of work than B and the ratio of time taken by A and B would be = 1 : 2 So, if there is a difference of one day (2–1), B takes 2 days As per question the difference in time taken by A and B is 40 days So, if the difference is of 40 days, B will take 2 × 40 = 80 days A takes 40 days less than B. So, A will take 40 days (80 – 40) to do the work. A’s one day work = 1/40 B’s one day work = 1/80 (A + B)’s one day work = (1/40) + ( 1/80) = 120/3200 = 3/80 So, working together will do the work in 80/3 days

#### 4. Question

A is twice as good as workman as B so he can do a work in 40 days less than B. If they work together. In how many days they cal do the work?

• a) 80/4 days

• b) 80/5 days

• c) 80/3 days

• d) 80/6 days

Answer: Option (c)

Explanation:

A is twice as good as workman as B so he will take less time to do a piece of work than B and the ratio of time taken by A and B would be = 1 : 2

So, if there is a difference of one day (2–1), B takes 2 days

As per question the difference in time taken by A and B is 40 days

So, if the difference is of 40 days, B will take 2 × 40 = 80 days

A takes 40 days less than B. So, A will take 40 days (80 – 40) to do the work.

A’s one day work = 1/40

B’s one day work = 1/80

(A + B)’s one day work = (1/40) + ( 1/80) = 120/3200 = 3/80

So, working together will do the work in 80/3 days

Answer: Option (c)

Explanation:

A is twice as good as workman as B so he will take less time to do a piece of work than B and the ratio of time taken by A and B would be = 1 : 2

So, if there is a difference of one day (2–1), B takes 2 days

As per question the difference in time taken by A and B is 40 days

So, if the difference is of 40 days, B will take 2 × 40 = 80 days

A takes 40 days less than B. So, A will take 40 days (80 – 40) to do the work.

A’s one day work = 1/40

B’s one day work = 1/80

(A + B)’s one day work = (1/40) + ( 1/80) = 120/3200 = 3/80

So, working together will do the work in 80/3 days

• Question 5 of 5 5. Question Seventy-six ladies complete a job in 33 days. Due to some reason, some ladies did not join the work, and therefore it was completed in 44 days. The number of ladies who did not report for the work is ? a) 19 b) 18 c) 17 d) 20 Correct Answer: Option (a) Explanation: Short Cut: W1 x D1 = W2 x D2 76 x 33 = (76-x) x 44 x = 19 Incorrect Answer: Option (a) Explanation: Short Cut: W1 x D1 = W2 x D2 76 x 33 = (76-x) x 44 x = 19

#### 5. Question

Seventy-six ladies complete a job in 33 days. Due to some reason, some ladies did not join the work, and therefore it was completed in 44 days. The number of ladies who did not report for the work is ?

Answer: Option (a)

Explanation:

Short Cut:

W1 x D1 = W2 x D2

76 x 33 = (76-x) x 44

x = 19

Answer: Option (a)

Explanation:

Short Cut:

W1 x D1 = W2 x D2

76 x 33 = (76-x) x 44

x = 19

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