UPSC Insta–DART (Daily Aptitude and Reasoning Test) 25 Sep 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 24 men and 32 boys can do a piece of work in 10 days and 26 men and 48 boys can do it in 8 days. What is the ratio of daily work done by a man with that by a boy? a) 3 : 1 b) 2 : 1 c) 5 : 6 d) 3 : 4 Correct Answer: Option (b) Explanation: 24 men + 32 boys can do the work in 10 days. So, 10 × (24 men + 32 boys) can do the work in 1 day. Or (240 men + 320 boys) can do the work in 1 day. Similarly 8 x (26 men + 48 boys) can do the same work in 1 day. Or (208 men + 384 boys) can do the same work in 1 day. So, 208 men + 384 boys = 240 men + 320 boys or 32 men = 64 boys or 1 man = 2 boys So, Ratio of daily work done by a man with that by a boy is 2 : 1. Incorrect Answer: Option (b) Explanation: 24 men + 32 boys can do the work in 10 days. So, 10 × (24 men + 32 boys) can do the work in 1 day. Or (240 men + 320 boys) can do the work in 1 day. Similarly 8 x (26 men + 48 boys) can do the same work in 1 day. Or (208 men + 384 boys) can do the same work in 1 day. So, 208 men + 384 boys = 240 men + 320 boys or 32 men = 64 boys or 1 man = 2 boys So, Ratio of daily work done by a man with that by a boy is 2 : 1.
#### 1. Question
24 men and 32 boys can do a piece of work in 10 days and 26 men and 48 boys can do it in 8 days. What is the ratio of daily work done by a man with that by a boy?
Answer: Option (b)
Explanation:
24 men + 32 boys can do the work in 10 days.
So, 10 × (24 men + 32 boys) can do the work in 1 day.
Or (240 men + 320 boys) can do the work in 1 day.
Similarly 8 x (26 men + 48 boys) can do the same work in 1 day.
Or (208 men + 384 boys) can do the same work in 1 day.
So, 208 men + 384 boys = 240 men + 320 boys
or 32 men = 64 boys
or 1 man = 2 boys
So, Ratio of daily work done by a man with that by a boy is 2 : 1.
Answer: Option (b)
Explanation:
24 men + 32 boys can do the work in 10 days.
So, 10 × (24 men + 32 boys) can do the work in 1 day.
Or (240 men + 320 boys) can do the work in 1 day.
Similarly 8 x (26 men + 48 boys) can do the same work in 1 day.
Or (208 men + 384 boys) can do the same work in 1 day.
So, 208 men + 384 boys = 240 men + 320 boys
or 32 men = 64 boys
or 1 man = 2 boys
So, Ratio of daily work done by a man with that by a boy is 2 : 1.
• Question 2 of 5 2. Question Jacob and Janardhan together can do a piece of work in 20 days, Jacob having worked for 14 days, Janardhan finishes the remaining work in 26 days. Doing alone, in how many days does Janardhan finishes the whole work? a) 40 days b) 30 days c) 45 days d) 60 days Correct Answer: Option (a) Explanation: As per the man day’s concept, here both Jacob and Janardhan are doing the same work in 20 days. So, 20 Jacob days + 20 Janardhan days = 14 Jacob days + 26 Janardhan days 6 Jacob days=6 Janardhan days Their efficiency is the same, hence either of them would take the double amount of time working alone than if they were doing together. Therefore, Janardhan will finish the whole work in 40 days if he is working alone. Incorrect Answer: Option (a) Explanation: As per the man day’s concept, here both Jacob and Janardhan are doing the same work in 20 days. So, 20 Jacob days + 20 Janardhan days = 14 Jacob days + 26 Janardhan days 6 Jacob days=6 Janardhan days Their efficiency is the same, hence either of them would take the double amount of time working alone than if they were doing together. Therefore, Janardhan will finish the whole work in 40 days if he is working alone.
#### 2. Question
Jacob and Janardhan together can do a piece of work in 20 days, Jacob having worked for 14 days, Janardhan finishes the remaining work in 26 days. Doing alone, in how many days does Janardhan finishes the whole work?
• a) 40 days
• b) 30 days
• c) 45 days
• d) 60 days
Answer: Option (a)
Explanation:
As per the man day’s concept, here both Jacob and Janardhan are doing the same work in 20 days.
So, 20 Jacob days + 20 Janardhan days = 14 Jacob days + 26 Janardhan days
6 Jacob days=6 Janardhan days
Their efficiency is the same, hence either of them would take the double amount of time working alone than if they were doing together.
Therefore, Janardhan will finish the whole work in 40 days if he is working alone.
Answer: Option (a)
Explanation:
As per the man day’s concept, here both Jacob and Janardhan are doing the same work in 20 days.
So, 20 Jacob days + 20 Janardhan days = 14 Jacob days + 26 Janardhan days
6 Jacob days=6 Janardhan days
Their efficiency is the same, hence either of them would take the double amount of time working alone than if they were doing together.
Therefore, Janardhan will finish the whole work in 40 days if he is working alone.
• Question 3 of 5 3. Question If 5 women and 3 girls can plough 23 acres in 4 days and if 3 women and 2 girls can plough 7 acres in 2 days, then how many girls must assist 7 women in order that they may plough 45 acres in 6 days? a) 2 b) 4 c) 5 d) 7 Correct Answer: Option (a) Explanation: 5 women + 3 girls can plough 23 acres in 4 days. 3 women + 2 girls can plough 7 acres in 2 days. 14 (5 women + 3 girls) can plough 23 x 14 acres in 4 days. 23 (3 women + 2 girls) can plough 7 x 2 x 23 acres in 4 days. 14 (5 women + 3 girls) = 23 (3 women + 2 girls). 1 woman = 4 girls. Now 5 women + 3 girls = 23 girls. 23 girls can plough 23 acres in 4 days. 30 girls can plough 45 acres in 6 days. But 30 girls = 28 girls + 2 girls = 7 women + 2 girls. Hence 2 girls must assist 7 women. So the work will be completed in 3 × 5 = 15 days. Incorrect Answer: Option (a) Explanation: 5 women + 3 girls can plough 23 acres in 4 days. 3 women + 2 girls can plough 7 acres in 2 days. 14 (5 women + 3 girls) can plough 23 x 14 acres in 4 days. 23 (3 women + 2 girls) can plough 7 x 2 x 23 acres in 4 days. 14 (5 women + 3 girls) = 23 (3 women + 2 girls). 1 woman = 4 girls. Now 5 women + 3 girls = 23 girls. 23 girls can plough 23 acres in 4 days. 30 girls can plough 45 acres in 6 days. But 30 girls = 28 girls + 2 girls = 7 women + 2 girls. Hence 2 girls must assist 7 women. So the work will be completed in 3 × 5 = 15 days.
#### 3. Question
If 5 women and 3 girls can plough 23 acres in 4 days and if 3 women and 2 girls can plough 7 acres in 2 days, then how many girls must assist 7 women in order that they may plough 45 acres in 6 days?
Answer: Option (a)
Explanation:
5 women + 3 girls can plough 23 acres in 4 days.
3 women + 2 girls can plough 7 acres in 2 days.
14 (5 women + 3 girls) can plough 23 x 14 acres in 4 days.
23 (3 women + 2 girls) can plough 7 x 2 x 23 acres in 4 days.
14 (5 women + 3 girls) = 23 (3 women + 2 girls).
1 woman = 4 girls. Now 5 women + 3 girls = 23 girls.
23 girls can plough 23 acres in 4 days.
30 girls can plough 45 acres in 6 days.
But 30 girls = 28 girls + 2 girls = 7 women + 2 girls.
Hence 2 girls must assist 7 women. So the work will be completed in 3 × 5 = 15 days.
Answer: Option (a)
Explanation:
5 women + 3 girls can plough 23 acres in 4 days.
3 women + 2 girls can plough 7 acres in 2 days.
14 (5 women + 3 girls) can plough 23 x 14 acres in 4 days.
23 (3 women + 2 girls) can plough 7 x 2 x 23 acres in 4 days.
14 (5 women + 3 girls) = 23 (3 women + 2 girls).
1 woman = 4 girls. Now 5 women + 3 girls = 23 girls.
23 girls can plough 23 acres in 4 days.
30 girls can plough 45 acres in 6 days.
But 30 girls = 28 girls + 2 girls = 7 women + 2 girls.
Hence 2 girls must assist 7 women. So the work will be completed in 3 × 5 = 15 days.
• Question 4 of 5 4. Question The ratio of the efficiencies of M and N is 7 : 5. Working together, they can complete a work in 45/2 days. Consider the following statements: M alone will complete 70% of the same work in 27 days. M alone will complete 40% of the same work in 15.4 days. Which of the above statements is/are correct? a) 1 only b) 2 only c) Both 1 and 2 d) Neither 1 nor 2 Correct Answer: Option (c) Explanation: Let the efficiency of M be 7x units/day. Then, efficiency of N = 5x units/day. Therefore, total work = (7x + 5x) × 45/2 = (12x) × 45/2 = 270x For statement1: 70% of work = (270x) × 70% = 189x Time taken by M to complete 70% work = 189x/7x = 27 days For Statement 2: 40% of work = (270x) × 40% = 108x Time taken by M to complete 40% work = 108x/7x = 15.4 days Therefore, both the statements are correct. Hence, option (c) is the correct answer. Incorrect Answer: Option (c) Explanation: Let the efficiency of M be 7x units/day. Then, efficiency of N = 5x units/day. Therefore, total work = (7x + 5x) × 45/2 = (12x) × 45/2 = 270x For statement1: 70% of work = (270x) × 70% = 189x Time taken by M to complete 70% work = 189x/7x = 27 days For Statement 2: 40% of work = (270x) × 40% = 108x Time taken by M to complete 40% work = 108x/7x = 15.4 days Therefore, both the statements are correct. Hence, option (c) is the correct answer.
#### 4. Question
The ratio of the efficiencies of M and N is 7 : 5. Working together, they can complete a work in 45/2 days.
Consider the following statements:
• M alone will complete 70% of the same work in 27 days.
• M alone will complete 40% of the same work in 15.4 days.
Which of the above statements is/are correct?
• c) Both 1 and 2
• d) Neither 1 nor 2
Answer: Option (c)
Explanation:
Let the efficiency of M be 7x units/day.
Then, efficiency of N = 5x units/day.
Therefore, total work = (7x + 5x) × 45/2 = (12x) × 45/2 = 270x
For statement1:
70% of work = (270x) × 70% = 189x
Time taken by M to complete 70% work = 189x/7x = 27 days
For Statement 2:
40% of work = (270x) × 40% = 108x
Time taken by M to complete 40% work = 108x/7x = 15.4 days
Therefore, both the statements are correct. Hence, option (c) is the correct answer.
Answer: Option (c)
Explanation:
Let the efficiency of M be 7x units/day.
Then, efficiency of N = 5x units/day.
Therefore, total work = (7x + 5x) × 45/2 = (12x) × 45/2 = 270x
For statement1:
70% of work = (270x) × 70% = 189x
Time taken by M to complete 70% work = 189x/7x = 27 days
For Statement 2:
40% of work = (270x) × 40% = 108x
Time taken by M to complete 40% work = 108x/7x = 15.4 days
Therefore, both the statements are correct. Hence, option (c) is the correct answer.
• Question 5 of 5 5. Question X can do a piece of work in d days, while Y can do the same work in (d+5) days. If X and Y together can do the whole work in 6 days, then efficiency of Z who can complete the same work in 5 days is how much percentage less/more than the efficiency of X a) 100% b) 55% c) 70% d) 25% Correct Answer: Option (a) Explanation: X can do a piece of work in d days, while Y can do the same work in (d+5) days. X’s 1 day work = 1/d Y’s 1 day work = 1/(d+ 5) X and Y together can do the whole work in 6 days. So, (X +Y)’s 1 day work = 1/6 According to the question, 1/d + 1/(d+5) = 1/6 Or 6(2d+5) = d (d+5) Or d2 – 7d – 30 = 0 Or d2 – 10d + 3d – 30 = 0 Or d (d – 10) +3(d – 10) = 0 Or (d – 10) (d + 3) = 0 So, d = 10 or – 3 (neglected, because number of days can’t be negative) So, d = 10 So, Time taken by X to do the whole work = d = 10 days Time taken by Y to do the whole work = d + 5 = 15 days Time taken by Z to do the whole work = 5 days (given) Let total amount of work = 30 units (LCM of 10, 15) Efficiency of X = 30/10 = 3 units/day Efficiency of Z = 30/5 = 6 units/day Required percentage = {(6 – 3)/3} × 100 = 100% more Hence, option (a) is the correct answer. Incorrect Answer: Option (a) Explanation: X can do a piece of work in d days, while Y can do the same work in (d+5) days. X’s 1 day work = 1/d Y’s 1 day work = 1/(d+ 5) X and Y together can do the whole work in 6 days. So, (X +Y)’s 1 day work = 1/6 According to the question, 1/d + 1/(d+5) = 1/6 Or 6(2d+5) = d (d+5) Or d2 – 7d – 30 = 0 Or d2 – 10d + 3d – 30 = 0 Or d (d – 10) +3(d – 10) = 0 Or (d – 10) (d + 3) = 0 So, d = 10 or – 3 (neglected, because number of days can’t be negative) So, d = 10 So, Time taken by X to do the whole work = d = 10 days Time taken by Y to do the whole work = d + 5 = 15 days Time taken by Z to do the whole work = 5 days (given) Let total amount of work = 30 units (LCM of 10, 15) Efficiency of X = 30/10 = 3 units/day Efficiency of Z = 30/5 = 6 units/day Required percentage = {(6 – 3)/3} × 100 = 100% more Hence, option (a) is the correct answer.
#### 5. Question
X can do a piece of work in d days, while Y can do the same work in (d+5) days. If X and Y together can do the whole work in 6 days, then efficiency of Z who can complete the same work in 5 days is how much percentage less/more than the efficiency of X
Answer: Option (a)
Explanation:
X can do a piece of work in d days, while Y can do the same work in (d+5) days.
X’s 1 day work = 1/d Y’s 1 day work = 1/(d+ 5)
X and Y together can do the whole work in 6 days.
So, (X +Y)’s 1 day work = 1/6
According to the question,
1/d + 1/(d+5) = 1/6
Or 6(2d+5) = d (d+5)
Or d2 – 7d – 30 = 0
Or d2 – 10d + 3d – 30 = 0
Or d (d – 10) +3(d – 10) = 0
Or (d – 10) (d + 3) = 0
So, d = 10 or – 3 (neglected, because number of days can’t be negative)
So, d = 10
So, Time taken by X to do the whole work = d = 10 days
Time taken by Y to do the whole work = d + 5 = 15 days
Time taken by Z to do the whole work = 5 days (given)
Let total amount of work = 30 units (LCM of 10, 15)
Efficiency of X = 30/10 = 3 units/day
Efficiency of Z = 30/5 = 6 units/day
Required percentage = {(6 – 3)/3} × 100 = 100% more
Hence, option (a) is the correct answer.
Answer: Option (a)
Explanation:
X can do a piece of work in d days, while Y can do the same work in (d+5) days.
X’s 1 day work = 1/d Y’s 1 day work = 1/(d+ 5)
X and Y together can do the whole work in 6 days.
So, (X +Y)’s 1 day work = 1/6
According to the question,
1/d + 1/(d+5) = 1/6
Or 6(2d+5) = d (d+5)
Or d2 – 7d – 30 = 0
Or d2 – 10d + 3d – 30 = 0
Or d (d – 10) +3(d – 10) = 0
Or (d – 10) (d + 3) = 0
So, d = 10 or – 3 (neglected, because number of days can’t be negative)
So, d = 10
So, Time taken by X to do the whole work = d = 10 days
Time taken by Y to do the whole work = d + 5 = 15 days
Time taken by Z to do the whole work = 5 days (given)
Let total amount of work = 30 units (LCM of 10, 15)
Efficiency of X = 30/10 = 3 units/day
Efficiency of Z = 30/5 = 6 units/day
Required percentage = {(6 – 3)/3} × 100 = 100% more
Hence, option (a) is the correct answer.
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