[Mission 2024] Insta–DART (Daily Aptitude and Reasoning Test) 30 April 2024

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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).

Wish you all the best ! 🙂

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• Question 1 of 5 1. Question If a:b = 3:5 and b:c = 7:8, then 2a:3b:7c is equal to (a) 42:105:320 (b) 15:21:40 (c) 6:15:40 (d) 30:21:350 Correct Ans: c We have, a/b = 3/5 Because b=5a/3 and b/c = 7/8 C=(8/7)a = (8/7)´(5a/3) = 40a/21 Because a:b:c = a:5a/3 :40a/21 Now, 2a:3b:7c=2a:5a:( 40a/3) = 2:5( 40a)/3 = 6:15:40 Incorrect Ans: c We have, a/b = 3/5 Because b=5a/3 and b/c = 7/8 C=(8/7)a = (8/7)´(5a/3) = 40a/21 Because a:b:c = a:5a/3 :40a/21 Now, 2a:3b:7c=2a:5a:( 40a/3) = 2:5( 40a)/3 = 6:15:40

#### 1. Question

If a:b = 3:5 and b:c = 7:8, then 2a:3b:7c is equal to

• (a) 42:105:320

• (b) 15:21:40

• (c) 6:15:40

• (d) 30:21:350

We have, a/b = 3/5

Because b=5a/3 and b/c = 7/8

C=(8/7)a = (8/7)´(5a/3) = 40a/21

Because a:b:c = a:5a/3 :40a/21

Now, 2a:3b:7c=2a:5a:( 40a/3) = 2:5( 40a)/3 = 6:15:40

We have, a/b = 3/5

Because b=5a/3 and b/c = 7/8

C=(8/7)a = (8/7)´(5a/3) = 40a/21

Because a:b:c = a:5a/3 :40a/21

Now, 2a:3b:7c=2a:5a:( 40a/3) = 2:5( 40a)/3 = 6:15:40

• Question 2 of 5 2. Question The speeds of three buses are in the ratio 2:3:4. The time taken by these buses to travel the same distance will be in ratio. (a) 2:3:4 (b) 4:3:2 (c) 4:3:6 (d) 6:4:3 Correct Ans: d Let the distance be x. Now, ratio of time taken the distance by each bus = x/2:x/3:x/4=12/2:12/3:12/4 = 6:4:3 Incorrect Ans: d Let the distance be x. Now, ratio of time taken the distance by each bus = x/2:x/3:x/4=12/2:12/3:12/4 = 6:4:3

#### 2. Question

The speeds of three buses are in the ratio 2:3:4. The time taken by these buses to travel the same distance will be in ratio.

Let the distance be x.

Now, ratio of time taken the distance by each bus

= x/2:x/3:x/4=12/2:12/3:12/4 = 6:4:3

Let the distance be x.

Now, ratio of time taken the distance by each bus

= x/2:x/3:x/4=12/2:12/3:12/4 = 6:4:3

• Question 3 of 5 3. Question In a mixture of milk and water of volume 30 L, the ratio of milk and water is 7:3. The quantity of water to be added to the mixture to make the ratio of milk and water 1:2 is (a) 30 L (b) 32L (c) 33L (d) 35L Correct Ans: c Since, milk = 7x and water = 3x Then, 7x + 3x = 30 10x = 30 \x = 3 So, milk= 21L and water = 9L Let y L of water to be added. Then, 21/(9+y) =1/2 9+y = 42 Y=33L Incorrect Ans: c Since, milk = 7x and water = 3x Then, 7x + 3x = 30 10x = 30 \x = 3 So, milk= 21L and water = 9L Let y L of water to be added. Then, 21/(9+y) =1/2 9+y = 42 Y=33L

#### 3. Question

In a mixture of milk and water of volume 30 L, the ratio of milk and water is 7:3. The quantity of water to be added to the mixture to make the ratio of milk and water 1:2 is

Since, milk = 7x and water = 3x

Then, 7x + 3x = 30

So, milk= 21L and water = 9L

Let y L of water to be added.

Then, 21/(9+y) =1/2

Since, milk = 7x and water = 3x

Then, 7x + 3x = 30

So, milk= 21L and water = 9L

Let y L of water to be added.

Then, 21/(9+y) =1/2

• Question 4 of 5 4. Question The ratio of ages of A and B is 2:5 and the ratio of ages of B and C is 3:4. What is the ratio of ages of A, B and C? (a) 6:15:20 (b) 8:5:3 (c) 6:5:4 (d) 2:15:4 Correct Ans: a Given, ratio of ages of A and B i.e A:B = 2:5 Ratio of ages of B and C = 3:4 \Ratio of ages of A,B and C = = 2 x 3:3x 5:5 x 4 = 6:15:20 Incorrect Ans: a Given, ratio of ages of A and B i.e A:B = 2:5 Ratio of ages of B and C = 3:4 \Ratio of ages of A,B and C = = 2 x 3:3x 5:5 x 4 = 6:15:20

#### 4. Question

The ratio of ages of A and B is 2:5 and the ratio of ages of B and C is 3:4. What is the ratio of ages of A, B and C?

• (a) 6:15:20

• (d) 2:15:4

Given, ratio of ages of A and B i.e A:B = 2:5

Ratio of ages of B and C = 3:4

\Ratio of ages of A,B and C =

= 2 x 3:3x 5:5 x 4 = 6:15:20

Given, ratio of ages of A and B i.e A:B = 2:5

Ratio of ages of B and C = 3:4

\Ratio of ages of A,B and C =

= 2 x 3:3x 5:5 x 4 = 6:15:20

• Question 5 of 5 5. Question (X+y) :(x-y)=3:5 and any xy = positive imply that A-X and y are both positive B-X and y are both negative C-One of them is positive and one of them is negative D-No real solution for x and y exist Correct Solution: B Ans:d Given that, (x+y):/9x-y)=3:5 \(x+y)/(x-y)=3/5 Applying componendo and dividend rule, we get [(x+y)+(x-y)]/[(x+y)-(x-y)] = (3+5)/(3-5) 2x/2y = 8/-2 x/y = -4 ∴x=-4y But it is given, xy = positive ∴-4yx y = Positive -4y2 = Positive, which is not possible Hence, no real solution for x and y exist. One person sits between T and J Incorrect Solution: B Ans:d Given that, (x+y):/9x-y)=3:5 \(x+y)/(x-y)=3/5 Applying componendo and dividend rule, we get [(x+y)+(x-y)]/[(x+y)-(x-y)] = (3+5)/(3-5) 2x/2y = 8/-2 x/y = -4 ∴x=-4y But it is given, xy = positive ∴-4yx y = Positive -4y2 = Positive, which is not possible Hence, no real solution for x and y exist. One person sits between T and J

#### 5. Question

(X+y) :(x-y)=3:5 and any xy = positive imply that

• A-X and y are both positive

• B-X and y are both negative

• C-One of them is positive and one of them is negative

• D-No real solution for x and y exist

Solution: B

Given that, (x+y):/9x-y)=3:5

\(x+y)/(x-y)=3/5

Applying componendo and dividend rule, we get

[(x+y)+(x-y)]/[(x+y)-(x-y)] = (3+5)/(3-5)

2x/2y = 8/-2

But it is given, xy = positive

∴-4yx y = Positive

-4y2 = Positive, which is not possible

Hence, no real solution for x and y exist.

One person sits between T and J