[Mission 2024] Insta–DART (Daily Aptitude and Reasoning Test) 3 May 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 p% of Rs. x is equal to t times q% of Rs. y, then what is the ratio of x to y? (a) pt : q (b) p : qt (c) qt : p (d) q : pt Correct Sol. (c) By given condition, p% of x = t (q % of y) ⇒xp/100 = (yq × t)/100 ⇒x/y = qt/p Hence, x : y = =qt : p Incorrect Sol. (c) By given condition, p% of x = t (q % of y) ⇒xp/100 = (yq × t)/100 ⇒x/y = qt/p Hence, x : y = =qt : p

#### 1. Question

If p% of Rs. x is equal to t times q% of Rs. y, then what is the ratio of x to y?

• (a) pt : q

• (b) p : qt

• (c) qt : p

• (d) q : pt

By given condition, p% of x = t (q % of y)

⇒xp/100 = (yq × t)/100

⇒x/y = qt/p

Hence, x : y = =qt : p

By given condition, p% of x = t (q % of y)

⇒xp/100 = (yq × t)/100

⇒x/y = qt/p

Hence, x : y = =qt : p

• Question 2 of 5 2. Question A bag contains Rs. 112 in the form of Rs. 1, 50 paise and 10 paise coins in the ratio 3 : 8 : 10. What is the number of 50 paise coins? (a) 112 (b) 108 (c) 96 (d) 84 Correct Sol. (a) Convert ratios in paise- 100 paise:50 paise:10paise Divide by 10 We ll get-10 : 5 : 1 and new as per given ratio we get new ratio as 10 × 3 : 5 × 8 : 1 × 8 = 30 : 40 : 10 = 3 : 4 : 1 ⇒3x + 4x + x = 112 ⇒x = 112/8 = 14 Hence, Number of 50 paise coins = 14 x 8 = 112. Incorrect Sol. (a) Convert ratios in paise- 100 paise:50 paise:10paise Divide by 10 We ll get-10 : 5 : 1 and new as per given ratio we get new ratio as 10 × 3 : 5 × 8 : 1 × 8 = 30 : 40 : 10 = 3 : 4 : 1 ⇒3x + 4x + x = 112 ⇒x = 112/8 = 14 Hence, Number of 50 paise coins = 14 x 8 = 112.

#### 2. Question

A bag contains Rs. 112 in the form of Rs. 1, 50 paise and 10 paise coins in the ratio 3 : 8 : 10. What is the number of 50 paise coins?

Convert ratios in paise-

100 paise:50 paise:10paise

Divide by 10

We ll get-10 : 5 : 1 and new as per given ratio we get new ratio as

10 × 3 : 5 × 8 : 1 × 8 = 30 : 40 : 10 = 3 : 4 : 1

⇒3x + 4x + x = 112

⇒x = 112/8 = 14

Hence, Number of 50 paise coins = 14 x 8 = 112.

Convert ratios in paise-

100 paise:50 paise:10paise

Divide by 10

We ll get-10 : 5 : 1 and new as per given ratio we get new ratio as

10 × 3 : 5 × 8 : 1 × 8 = 30 : 40 : 10 = 3 : 4 : 1

⇒3x + 4x + x = 112

⇒x = 112/8 = 14

Hence, Number of 50 paise coins = 14 x 8 = 112.

• Question 3 of 5 3. Question The speeds of three cars are in the ratio 4 : 3 : 2. What is the ratio between the time taken by the cars to cover the same distance? (a) 2 : 3 : 4 (b) 3 : 4 : 6 (c) 1 : 2 : 3 (d) 4 : 3 : 2 Correct Sol. (b) Speed ∞ 1/Time Hence, Required ratio = 1/4 : 1/3 : 1/2 = 3 : 4 : 6 Incorrect Sol. (b) Speed ∞ 1/Time Hence, Required ratio = 1/4 : 1/3 : 1/2 = 3 : 4 : 6

#### 3. Question

The speeds of three cars are in the ratio 4 : 3 : 2. What is the ratio between the time taken by the cars to cover the same distance?

• (a) 2 : 3 : 4

• (b) 3 : 4 : 6

• (c) 1 : 2 : 3

• (d) 4 : 3 : 2

Speed ∞ 1/Time

Hence, Required ratio = 1/4 : 1/3 : 1/2 = 3 : 4 : 6

Speed ∞ 1/Time

Hence, Required ratio = 1/4 : 1/3 : 1/2 = 3 : 4 : 6

• Question 4 of 5 4. Question What is the ratio between times taken by a train 240 m long to cross an electric pole and a bridge of 80 m length? (a) 2 : 3 (b) 3 : 4 (c) 4 : 5 (d) 5 : 6 Correct Sol. (b) Since, the speed of train is constant, then D1/T1 = D2/T2 240/T1 = (240 + 80)/T2 T1/T2 = 240/320 ⇒T1 : T2 = 3 : 4 Incorrect Sol. (b) Since, the speed of train is constant, then D1/T1 = D2/T2 240/T1 = (240 + 80)/T2 T1/T2 = 240/320 ⇒T1 : T2 = 3 : 4

#### 4. Question

What is the ratio between times taken by a train 240 m long to cross an electric pole and a bridge of 80 m length?

Since, the speed of train is constant, then

D1/T1 = D2/T2

240/T1 = (240 + 80)/T2

T1/T2 = 240/320

⇒T1 : T2 = 3 : 4

Since, the speed of train is constant, then

D1/T1 = D2/T2

240/T1 = (240 + 80)/T2

T1/T2 = 240/320

⇒T1 : T2 = 3 : 4

• Question 5 of 5 5. Question ‘X’ is twice as old as ‘Y’ 3 yr ago, when ‘X’ was as old as ‘Y’ today. If the difference between their ages at present is 3 yr, how old is ‘X’ at present? (a) 18 yr (b) 12 yr (c) 9 yr (d) 8 yr Correct Sol. (c) Let present age of X = x yr and present age of Y = (x – 3) yr 3 yr ago, age of X = (x – 3) yr and age of Y = (x – 6) yr According to the question, x – 3 = 2(x – 6) ⇒x – 3 = 2x – 12 ⇒12 – 3 = 2x – x ⇒x = 9yr Incorrect Sol. (c) Let present age of X = x yr and present age of Y = (x – 3) yr 3 yr ago, age of X = (x – 3) yr and age of Y = (x – 6) yr According to the question, x – 3 = 2(x – 6) ⇒x – 3 = 2x – 12 ⇒12 – 3 = 2x – x ⇒x = 9yr

#### 5. Question

‘X’ is twice as old as ‘Y’ 3 yr ago, when ‘X’ was as old as ‘Y’ today. If the difference between their ages at present is 3 yr, how old is ‘X’ at present?

Let present age of X = x yr

and present age of Y = (x – 3) yr

3 yr ago, age of X = (x – 3) yr

and age of Y = (x – 6) yr

According to the question, x – 3 = 2(x – 6)

⇒x – 3 = 2x – 12

⇒12 – 3 = 2x – x