UPSC Insta–DART (Daily Aptitude and Reasoning Test) 16 Aug 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 An enterprise got a bonus and decided to share it in equal parts between the exemplary workers. It turned out, however, that there were three more exemplary workers than it had been assumed. In that case, each of them would have got 74 less. The administration had found the possibility to increase the total sum of the bonus by 790 and as a result each exemplary worker received 725. How many people received the bonus? (a) 9 (b) 8 (c) 18 (d) 16 Correct Solution:- Let the bonus be x Number of workers be n x/(n+3)=x/n -4 à 1 (x+90)/(n+3)=25 à2 By 2 we get x=25n-15 Substitute in 1 the value of x We get 4n^2-63n+45=0 By solving quadratic equation n=15 Total number of workers = n+3= 15+3=18 Option c is correct Incorrect Solution:- Let the bonus be x Number of workers be n x/(n+3)=x/n -4 à 1 (x+90)/(n+3)=25 à2 By 2 we get x=25n-15 Substitute in 1 the value of x We get 4n^2-63n+45=0 By solving quadratic equation n=15 Total number of workers = n+3= 15+3=18 Option c is correct

#### 1. Question

An enterprise got a bonus and decided to share it in equal parts between the exemplary workers. It turned out, however, that there were three more exemplary workers than it had been assumed. In that case, each of them would have got 74 less. The administration had found the possibility to increase the total sum of the bonus by 790 and as a result each exemplary worker received 725. How many people received the bonus?

Solution:-

Let the bonus be x

Number of workers be n

x/(n+3)=x/n -4 à 1

(x+90)/(n+3)=25 à2

By 2 we get x=25n-15

Substitute in 1 the value of x

We get 4n^2-63n+45=0

By solving quadratic equation n=15

Total number of workers = n+3= 15+3=18

Option c is correct

Solution:-

Let the bonus be x

Number of workers be n

x/(n+3)=x/n -4 à 1

(x+90)/(n+3)=25 à2

By 2 we get x=25n-15

Substitute in 1 the value of x

We get 4n^2-63n+45=0

By solving quadratic equation n=15

Total number of workers = n+3= 15+3=18

Option c is correct

• Question 2 of 5 2. Question In a class, the number of people who scored 61 or more is 30 and there are at most 39 people who scored below 61 marks. If the average marks of the class is 48, what is the largest possible average marks of the people who scored below 61 marks? (a) 38 (b) 35 (c) 32 (d) None of these Correct The total number of students is 69 (with x=39students scoring below 61). The total class marks are 48×69=3312, and the total marks for students scoring 61 or more is 1830. Thus, the total marks for students scoring below 61 is 3312−1830=1482. The largest possible average for these students is 1482/39 = 38391482=38. Correct option is A 38 Incorrect The total number of students is 69 (with x=39students scoring below 61). The total class marks are 48×69=3312, and the total marks for students scoring 61 or more is 1830. Thus, the total marks for students scoring below 61 is 3312−1830=1482. The largest possible average for these students is 1482/39 = 38391482=38. Correct option is A 38

#### 2. Question

In a class, the number of people who scored 61 or more is 30 and there are at most 39 people who scored below 61 marks. If the average marks of the class is 48, what is the largest possible average marks of the people who scored below 61 marks?

• (d) None of these

The total number of students is 69 (with x=39students scoring below 61). The total class marks are 48×69=3312, and the total marks for students scoring 61 or more is 1830. Thus, the total marks for students scoring below 61 is 3312−1830=1482. The largest possible average for these students is 1482/39 = 38391482=38.

Correct option is A 38

• Question 3 of 5 3. Question A team of miners planned to mine 1800 tons of ore during a certain number of days. Due to technical difficulties in one-third of the planned number of days, the team was able to achieve an output of 20 tons of ore less than the planned output. To make up for this, the team overachieved for the rest of the days by 20 tons. The end result was that the team completed the task one day ahead of time. How many tons of ore did the team initially plan to ore per day? (a) 50 tons (b) 100 tons (c) 150 tons (d) 200 tons. Correct Let the planned number of days be 3d and the planned output per day be x. From the equation 3d×x=1800 we find that x is the planned daily output. For the first d days, the output was x−20 and for the next 2d−1 days, the output was x+20 Setting up and solving the equation d(x−20)+(2d−1)(x+20)=1800 X^2+20X−12000 Solving this gives x=100 Thus, the initial planned daily output is option b 100 tons. Incorrect Let the planned number of days be 3d and the planned output per day be x. From the equation 3d×x=1800 we find that x is the planned daily output. For the first d days, the output was x−20 and for the next 2d−1 days, the output was x+20 Setting up and solving the equation d(x−20)+(2d−1)(x+20)=1800 X^2+20X−12000 Solving this gives x=100 Thus, the initial planned daily output is option b 100 tons.

#### 3. Question

A team of miners planned to mine 1800 tons of ore during a certain number of days. Due to technical difficulties in one-third of the planned number of days, the team was able to achieve an output of 20 tons of ore less than the planned output. To make up for this, the team overachieved for the rest of the days by 20 tons. The end result was that the team completed the task one day ahead of time. How many tons of ore did the team initially plan to ore per day?

• (a) 50 tons

• (b) 100 tons

• (c) 150 tons

• (d) 200 tons.

Let the planned number of days be 3d and the planned output per day be x.

From the equation 3d×x=1800 we find that x is the planned daily output.

For the first d days, the output was x−20 and for the next 2d−1 days, the output was x+20

Setting up and solving the equation d(x−20)+(2d−1)(x+20)=1800

X^2+20X−12000

Solving this gives x=100

Thus, the initial planned daily output is option b 100 tons.

Let the planned number of days be 3d and the planned output per day be x.

From the equation 3d×x=1800 we find that x is the planned daily output.

For the first d days, the output was x−20 and for the next 2d−1 days, the output was x+20

Setting up and solving the equation d(x−20)+(2d−1)(x+20)=1800

X^2+20X−12000

Solving this gives x=100

Thus, the initial planned daily output is option b 100 tons.

• Question 4 of 5 4. Question According to a plan, a team of woodcutters decided to harvest 216 m’ of wheat in several days. In the first three days, the team fulfilled the daily assignment, and then it harvested 8 m of wheat over and above the plan everyday. Therefore, a day before the planned date, they had already harvested 232 m’ of wheat. How many cubic metres of wheat a day did the team have to cut according to the plan? (a) 12cubic metre (b) 13 cubic metre (c) 24 cubic metre (d) 25. cubic metre. Correct The plan requires n days to cut 216 m³ of wood, so the planned daily output is 216/n First 3 days: The team cuts 3×(216/n) Remaining days: The team cuts 216/n+8 per day for n−4 days. The total harvested was 232 m³ 3×216/n + (n−4) × (216/n+8) = 232 By solving the quadratic equation n=9. The daily assignment was 216/9 = 24 cubic metres Incorrect The plan requires n days to cut 216 m³ of wood, so the planned daily output is 216/n First 3 days: The team cuts 3×(216/n) Remaining days: The team cuts 216/n+8 per day for n−4 days. The total harvested was 232 m³ 3×216/n + (n−4) × (216/n+8) = 232 By solving the quadratic equation n=9. The daily assignment was 216/9 = 24 cubic metres

#### 4. Question

According to a plan, a team of woodcutters decided to harvest 216 m’ of wheat in several days. In the first three days, the team fulfilled the daily assignment, and then it harvested 8 m of wheat over and above the plan everyday. Therefore, a day before the planned date, they had already harvested 232 m’ of wheat. How many cubic metres of wheat a day did the team have to cut according to the plan?

• (a) 12cubic metre

• (b) 13 cubic metre

• (c) 24 cubic metre

• (d) 25. cubic metre.

The plan requires n days to cut 216 m³ of wood, so the planned daily output is 216/n

First 3 days: The team cuts 3×(216/n)

Remaining days: The team cuts 216/n+8 per day for n−4 days.

The total harvested was 232 m³

3×216/n + (n−4) × (216/n+8) = 232

By solving the quadratic equation n=9.

The daily assignment was 216/9 = 24 cubic metres

The plan requires n days to cut 216 m³ of wood, so the planned daily output is 216/n

First 3 days: The team cuts 3×(216/n)

Remaining days: The team cuts 216/n+8 per day for n−4 days.

The total harvested was 232 m³

3×216/n + (n−4) × (216/n+8) = 232

By solving the quadratic equation n=9.

The daily assignment was 216/9 = 24 cubic metres

• Question 5 of 5 5. Question One collective farm got an average harvest of 21 tons of wheat per hectare and another collective farm that had 12 acres of land less given to wheat, got 25 tons from a hectare. As a result, the second farm harvested 300 tons of wheat more than the first. How many tons of wheat did each farm harvest? (a) 3150, 3450 (b) 3250, 3550 (c) 2150, 2450 (d) None of these Correct Solution. Using options check trial and error. Option A is correct Incorrect Solution. Using options check trial and error. Option A is correct

#### 5. Question

One collective farm got an average harvest of 21 tons of wheat per hectare and another collective farm that had 12 acres of land less given to wheat, got 25 tons from a hectare. As a result, the second farm harvested 300 tons of wheat more than the first. How many tons of wheat did each farm harvest?

• (a) 3150, 3450

• (b) 3250, 3550

• (c) 2150, 2450

• (d) None of these

Using options check trial and error.

Option A is correct

Using options check trial and error.

Option A is correct

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