[Mission 2024] Insta–DART (Daily Aptitude and Reasoning Test) 6 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 A certain amount of money has been divided between two persons P and Q in the ratio 3 : 5. But it was divided in the ratio of 2 : 3 and thereby Q loses Rs. 10. What was the amount? (a) Rs. 250 (b) Rs. 300 (c) Rs. 350 (d) Rs. 400 Correct Sol. (d) Let the amount be Rs. x. In first condition, Q’s part = 5x/(5+3) = 5x/8 In second condition, Q’s part = 3x/(2+3) = 3x/5 By given condition, 5x/8 – 3x/5 = 10 ⇒x/40 = 10 ⇒x = Rs. 400 Incorrect Sol. (d) Let the amount be Rs. x. In first condition, Q’s part = 5x/(5+3) = 5x/8 In second condition, Q’s part = 3x/(2+3) = 3x/5 By given condition, 5x/8 – 3x/5 = 10 ⇒x/40 = 10 ⇒x = Rs. 400

#### 1. Question

A certain amount of money has been divided between two persons P and Q in the ratio 3 : 5. But it was divided in the ratio of 2 : 3 and thereby Q loses Rs. 10. What was the amount?

• (a) Rs. 250

• (b) Rs. 300

• (c) Rs. 350

• (d) Rs. 400

Let the amount be Rs. x.

In first condition, Q’s part = 5x/(5+3) = 5x/8

In second condition, Q’s part = 3x/(2+3) = 3x/5

By given condition, 5x/8 – 3x/5 = 10

⇒x/40 = 10

⇒x = Rs. 400

Let the amount be Rs. x.

In first condition, Q’s part = 5x/(5+3) = 5x/8

In second condition, Q’s part = 3x/(2+3) = 3x/5

By given condition, 5x/8 – 3x/5 = 10

⇒x/40 = 10

⇒x = Rs. 400

• Question 2 of 5 2. Question If x varies as the mth power of y, y varies as nth power of z and x varies as the pth power of z, then which one of the following is correct? (a) p = m + n (b) p = m - n (c) p = mn (d) None of these Correct Sol. (c) x ∝ym ……(i) y ∝zn ……(ii) x ∝zp ……(iii) On putting the values of x and y from Eqs. (ii) and (iii) in Eq. (i), we get zp ∝ (zn)m ⇒z p ∝zmn ⇒p = mn Incorrect Sol. (c) x ∝ym ……(i) y ∝zn ……(ii) x ∝zp ……(iii) On putting the values of x and y from Eqs. (ii) and (iii) in Eq. (i), we get zp ∝ (zn)m ⇒z p ∝zmn ⇒p = mn

#### 2. Question

If x varies as the mth power of y, y varies as nth power of z and x varies as the pth power of z, then which one of the following is correct?

• (a) p = m + n

• (b) p = m - n

• (c) p = mn

• (d) None of these

x ∝ym ……(i)

y ∝zn ……(ii)

x ∝zp ……(iii)

On putting the values of x and y from Eqs. (ii) and (iii) in Eq. (i),

we get zp ∝ (zn)m

x ∝ym ……(i)

y ∝zn ……(ii)

x ∝zp ……(iii)

On putting the values of x and y from Eqs. (ii) and (iii) in Eq. (i),

we get zp ∝ (zn)m

• Question 3 of 5 3. Question The ratio between the ages of A and B is 2 : 5. After 8 yr, their ages will be in the ratio 1 : 2. What is the difference between their present ages? (a) 20 yr (b) 22 yr (c) 24 yr (d) 25 yr Correct Sol. (c) Let the ages of A and B be 2x and 5x yr respectively. By given condition, (2x + 8)/(5x + 8)=1/2 = 4x + 16 = 5x + 8 x => 8 Hence, Difference between their present ages = 5x – 2x = 3x = 3 × 8 = 24 yr. Incorrect Sol. (c) Let the ages of A and B be 2x and 5x yr respectively. By given condition, (2x + 8)/(5x + 8)=1/2 = 4x + 16 = 5x + 8 x => 8 Hence, Difference between their present ages = 5x – 2x = 3x = 3 × 8 = 24 yr.

#### 3. Question

The ratio between the ages of A and B is 2 : 5. After 8 yr, their ages will be in the ratio 1 : 2. What is the difference between their present ages?

Let the ages of A and B be 2x and 5x yr respectively.

By given condition, (2x + 8)/(5x + 8)=1/2

= 4x + 16 = 5x + 8 x => 8

Hence, Difference between their present ages = 5x – 2x = 3x

= 3 × 8 = 24 yr.

Let the ages of A and B be 2x and 5x yr respectively.

By given condition, (2x + 8)/(5x + 8)=1/2

= 4x + 16 = 5x + 8 x => 8

Hence, Difference between their present ages = 5x – 2x = 3x

= 3 × 8 = 24 yr.

• Question 4 of 5 4. Question A mixture contains milk and water in the ratio 5 : 1. On adding 5 L of water, the ratio of milk and water becomes 5 : 2. What is the quantity of milk in the original mixture? (a) 5 L (b) 25 L (c) 27.5 L (d) 32.5L Correct Sol. (b) Let quantities of milk and water be 5x and x L respectively. By given condition, 5x/(x + 5) = 5/2 ⇒10x = 5x + 25 ⇒5x = 25 ⇒X = 5 Hence, the quantity of milk in the original mixture = 5 × 5 = 25 L. Incorrect Sol. (b) Let quantities of milk and water be 5x and x L respectively. By given condition, 5x/(x + 5) = 5/2 ⇒10x = 5x + 25 ⇒5x = 25 ⇒X = 5 Hence, the quantity of milk in the original mixture = 5 × 5 = 25 L.

#### 4. Question

A mixture contains milk and water in the ratio 5 : 1. On adding 5 L of water, the ratio of milk and water becomes 5 : 2. What is the quantity of milk in the original mixture?

• (c) 27.5 L

Let quantities of milk and water be 5x and x L respectively.

By given condition,

5x/(x + 5) = 5/2

⇒10x = 5x + 25

Hence, the quantity of milk in the original mixture = 5 × 5 = 25 L.

Let quantities of milk and water be 5x and x L respectively.

By given condition,

5x/(x + 5) = 5/2

⇒10x = 5x + 25

Hence, the quantity of milk in the original mixture = 5 × 5 = 25 L.

• Question 5 of 5 5. Question The wages of labourers in a factory has increased in the ratio 22 : 25 and their number decreased in the ratio 3 : 2. What was the original wage bill of the factory, if the present bill is Rs. 5000? (a) Rs. 4000 (b) Rs. 6000 (c) Rs. 8000 (d) None of these Correct Sol.(d) Let initial salary = Rs. 22x and final salary = Rs. 25x Let initial number of employees = 3y and final number of employees = 2y Hence, Present bill = Final salary × Final number of employees ⇒5000 = 25x × 2y ⇒5000/50 = xy ⇒xy = 100. Hence, Original bill = Initial salary × Initial number of employees ⇒22x × 3y = 66xy ⇒66 × 100 = Rs. 6600 Incorrect Sol.(d) Let initial salary = Rs. 22x and final salary = Rs. 25x Let initial number of employees = 3y and final number of employees = 2y Hence, Present bill = Final salary × Final number of employees ⇒5000 = 25x × 2y ⇒5000/50 = xy ⇒xy = 100. Hence, Original bill = Initial salary × Initial number of employees ⇒22x × 3y = 66xy ⇒66 × 100 = Rs. 6600

#### 5. Question

The wages of labourers in a factory has increased in the ratio 22 : 25 and their number decreased in the ratio 3 : 2. What was the original wage bill of the factory, if the present bill is Rs. 5000?

• (a) Rs. 4000

• (b) Rs. 6000

• (c) Rs. 8000

• (d) None of these

Let initial salary = Rs. 22x

and final salary = Rs. 25x

Let initial number of employees = 3y

and final number of employees = 2y

Hence, Present bill = Final salary × Final number of employees

⇒5000 = 25x × 2y

⇒5000/50 = xy

⇒xy = 100.

Hence, Original bill = Initial salary × Initial number of employees

⇒22x × 3y = 66xy

⇒66 × 100 = Rs. 6600