Subject: ASF Assistant Director Past Papers

Explanation
The result of the expression 4 3 − 4 2 2 2 4^3 - frac{4^2}{2^2} ​ is 60. ​

Explanation
Paid= 3/5 Remaining = 1 – 3/5 = 2/5 Given conditions : 2/5 x Total amount = 400 ⇒        Total amount = 1000

Explanation
Let the two numbers be x and y. Given: x + y = 2490 ... (Equation 1) Also, 6.5% of x = 8.5% of y To simplify, convert percentages to decimals : 0.065x = 0.085y Now, divide both sides by 0.065: x = (0.085/0.065)y x = (85/65)y x = (17/13)y ... (Equation 2) Now, substitute Equation 2 into Equation 1: (17/13)y + y = 2490 Combine like terms: (30/13)y = 2490 Multiply both sides by 13/30: y = 1079 Now that we have found y, we can find x: x = 2490 - y (from Equation 1) x = 2490 - 1079 x = 1411 So, the correct answer is: 1411, 1079

Explanation
Let the total distance be x km . The man covers half the distance at 6 km/hr, so the time taken to cover this half is: Time = Distance / Speed = (x/2) / 6 = x/12 The man covers the remaining half at 3 km/hr, so the time taken to cover this half is: Time = Distance / Speed = (x/2) / 3 = x/6 The total time taken to cover the entire distance is the sum of the times taken to cover each half : Total Time = x/12 + x/6 To add these fractions, we need a common denominator, which is 12. So we can rewrite the fractions as: Total Time = x/12 + 2x/12 = 3x/12 = x/4 Now, we can find the average speed: Average Speed = Total Distance / Total Time = x / (x/4) = 4 km/hr So, the correct answer is: 4 km/hr

Explanation
Let the present age of the baby be x. After 20 years, the baby's age will be x + 20. According to the problem, the baby's age after 20 years will be 5 times the present age , so we can set up the equation: x + 20 = 5x Subtract x from both sides: 20 = 4x Divide both sides by 4: 5 = x So, the present age of the baby is 5 years.

Explanation
Total marks of 28 students in Mathematics = 28 x 50 = 1400 New number of students = 28 - 8 = 20 New average of marks in Mathematics = 50 + 5 = 55 ∴ Total marks of 20 students in Mathematics = 20 x 55 = 1100 ∴ Total marks of 8 students who left the school = 1400 - 1100 = 300 ∴ Average marks of these 8 students =  300/8 = 37.5

Explanation
Total marks of 28 students in Mathematics = 28 x 50 = 1400 New number of students = 28 - 8 = 20 New average of marks in Mathematics = 50 + 5 = 55 ∴ Total marks of 20 students in Mathematics = 20 x 55 = 1100 ∴ Total marks of 8 students who left the school = 1400 - 1100 = 300 ∴ Average marks of these 8 students =  300/8 = 37.5

Explanation
For one digit number 1 to 9 →1 × 9 = 9 For two digit number 10 to 99 → 2 × 90 = 180 For three digit number 100 to 300 →3 × 201 = 603 Hence, total number of required digits = 9 + 180 + 603  =  792

Explanation

Explanation
A complete day i.e 24 hours is 100%. 24 hours = 24 × 60 minutes = 1440 mins 4 hours, 30 mins = 270 mins 1440 mins = 100% of the day 270 mins = ? = 270 × 100 / 1440 = 18.75% 4 hours and 30 minutes is 18.75% of a day.

Explanation
Total age of new players = Total age of replaced players - Total decrease in age of all players  Total age of new players = 17 + 20 - (11 × 2)/12 ⇒ Total age of new players = 37 - (11/6) ⇒ Total age of new players = (222 - 11)/6 ⇒ Total age of new players = 211/6 ⇒ The Average age of two new players = 211/12 ∴ The average age of two new players is 17 years 7 months.

Explanation
The result of the expression 4 3 − 4 2 2 2 4^3 - frac{4^2}{2^2} ​ is 60. ​

Explanation
Paid= 3/5 Remaining = 1 – 3/5 = 2/5 Given conditions : 2/5 x Total amount = 400 ⇒        Total amount = 1000

Explanation
Let the two numbers be x and y. Given: x + y = 2490 ... (Equation 1) Also, 6.5% of x = 8.5% of y To simplify, convert percentages to decimals : 0.065x = 0.085y Now, divide both sides by 0.065: x = (0.085/0.065)y x = (85/65)y x = (17/13)y ... (Equation 2) Now, substitute Equation 2 into Equation 1: (17/13)y + y = 2490 Combine like terms: (30/13)y = 2490 Multiply both sides by 13/30: y = 1079 Now that we have found y, we can find x: x = 2490 - y (from Equation 1) x = 2490 - 1079 x = 1411 So, the correct answer is: 1411, 1079

Explanation
Let the total distance be x km . The man covers half the distance at 6 km/hr, so the time taken to cover this half is: Time = Distance / Speed = (x/2) / 6 = x/12 The man covers the remaining half at 3 km/hr, so the time taken to cover this half is: Time = Distance / Speed = (x/2) / 3 = x/6 The total time taken to cover the entire distance is the sum of the times taken to cover each half : Total Time = x/12 + x/6 To add these fractions, we need a common denominator, which is 12. So we can rewrite the fractions as: Total Time = x/12 + 2x/12 = 3x/12 = x/4 Now, we can find the average speed: Average Speed = Total Distance / Total Time = x / (x/4) = 4 km/hr So, the correct answer is: 4 km/hr

Explanation
Let the present age of the baby be x. After 20 years, the baby's age will be x + 20. According to the problem, the baby's age after 20 years will be 5 times the present age , so we can set up the equation: x + 20 = 5x Subtract x from both sides: 20 = 4x Divide both sides by 4: 5 = x So, the present age of the baby is 5 years.

Explanation
Total marks of 28 students in Mathematics = 28 x 50 = 1400 New number of students = 28 - 8 = 20 New average of marks in Mathematics = 50 + 5 = 55 ∴ Total marks of 20 students in Mathematics = 20 x 55 = 1100 ∴ Total marks of 8 students who left the school = 1400 - 1100 = 300 ∴ Average marks of these 8 students =  300/8 = 37.5

Explanation
For one digit number 1 to 9 →1 × 9 = 9 For two digit number 10 to 99 → 2 × 90 = 180 For three digit number 100 to 300 →3 × 201 = 603 Hence, total number of required digits = 9 + 180 + 603  =  792

Explanation

Explanation
A complete day i.e 24 hours is 100%. 24 hours = 24 × 60 minutes = 1440 mins 4 hours, 30 mins = 270 mins 1440 mins = 100% of the day 270 mins = ? = 270 × 100 / 1440 = 18.75% 4 hours and 30 minutes is 18.75% of a day.

Explanation
Total age of new players = Total age of replaced players - Total decrease in age of all players  Total age of new players = 17 + 20 - (11 × 2)/12 ⇒ Total age of new players = 37 - (11/6) ⇒ Total age of new players = (222 - 11)/6 ⇒ Total age of new players = 211/6 ⇒ The Average age of two new players = 211/12 ∴ The average age of two new players is 17 years 7 months.

Explanation
The result of the expression 4 3 − 4 2 2 2 4^3 - frac{4^2}{2^2} ​ is 60. ​

Explanation
Paid= 3/5 Remaining = 1 – 3/5 = 2/5 Given conditions : 2/5 x Total amount = 400 ⇒        Total amount = 1000

Explanation
Let the two numbers be x and y. Given: x + y = 2490 ... (Equation 1) Also, 6.5% of x = 8.5% of y To simplify, convert percentages to decimals : 0.065x = 0.085y Now, divide both sides by 0.065: x = (0.085/0.065)y x = (85/65)y x = (17/13)y ... (Equation 2) Now, substitute Equation 2 into Equation 1: (17/13)y + y = 2490 Combine like terms: (30/13)y = 2490 Multiply both sides by 13/30: y = 1079 Now that we have found y, we can find x: x = 2490 - y (from Equation 1) x = 2490 - 1079 x = 1411 So, the correct answer is: 1411, 1079

Explanation
Let the total distance be x km . The man covers half the distance at 6 km/hr, so the time taken to cover this half is: Time = Distance / Speed = (x/2) / 6 = x/12 The man covers the remaining half at 3 km/hr, so the time taken to cover this half is: Time = Distance / Speed = (x/2) / 3 = x/6 The total time taken to cover the entire distance is the sum of the times taken to cover each half : Total Time = x/12 + x/6 To add these fractions, we need a common denominator, which is 12. So we can rewrite the fractions as: Total Time = x/12 + 2x/12 = 3x/12 = x/4 Now, we can find the average speed: Average Speed = Total Distance / Total Time = x / (x/4) = 4 km/hr So, the correct answer is: 4 km/hr

Explanation
Let the present age of the baby be x. After 20 years, the baby's age will be x + 20. According to the problem, the baby's age after 20 years will be 5 times the present age , so we can set up the equation: x + 20 = 5x Subtract x from both sides: 20 = 4x Divide both sides by 4: 5 = x So, the present age of the baby is 5 years.

Explanation
Total marks of 28 students in Mathematics = 28 x 50 = 1400 New number of students = 28 - 8 = 20 New average of marks in Mathematics = 50 + 5 = 55 ∴ Total marks of 20 students in Mathematics = 20 x 55 = 1100 ∴ Total marks of 8 students who left the school = 1400 - 1100 = 300 ∴ Average marks of these 8 students =  300/8 = 37.5

Explanation
For one digit number 1 to 9 →1 × 9 = 9 For two digit number 10 to 99 → 2 × 90 = 180 For three digit number 100 to 300 →3 × 201 = 603 Hence, total number of required digits = 9 + 180 + 603  =  792

Explanation

Explanation
A complete day i.e 24 hours is 100%. 24 hours = 24 × 60 minutes = 1440 mins 4 hours, 30 mins = 270 mins 1440 mins = 100% of the day 270 mins = ? = 270 × 100 / 1440 = 18.75% 4 hours and 30 minutes is 18.75% of a day.

Explanation
Total age of new players = Total age of replaced players - Total decrease in age of all players  Total age of new players = 17 + 20 - (11 × 2)/12 ⇒ Total age of new players = 37 - (11/6) ⇒ Total age of new players = (222 - 11)/6 ⇒ Total age of new players = 211/6 ⇒ The Average age of two new players = 211/12 ∴ The average age of two new players is 17 years 7 months.

Explanation
The result of the expression 4 3 − 4 2 2 2 4^3 - frac{4^2}{2^2} ​ is 60. ​

Explanation
Paid= 3/5 Remaining = 1 – 3/5 = 2/5 Given conditions : 2/5 x Total amount = 400 ⇒        Total amount = 1000

Explanation
Let the two numbers be x and y. Given: x + y = 2490 ... (Equation 1) Also, 6.5% of x = 8.5% of y To simplify, convert percentages to decimals : 0.065x = 0.085y Now, divide both sides by 0.065: x = (0.085/0.065)y x = (85/65)y x = (17/13)y ... (Equation 2) Now, substitute Equation 2 into Equation 1: (17/13)y + y = 2490 Combine like terms: (30/13)y = 2490 Multiply both sides by 13/30: y = 1079 Now that we have found y, we can find x: x = 2490 - y (from Equation 1) x = 2490 - 1079 x = 1411 So, the correct answer is: 1411, 1079

Explanation
Let the total distance be x km . The man covers half the distance at 6 km/hr, so the time taken to cover this half is: Time = Distance / Speed = (x/2) / 6 = x/12 The man covers the remaining half at 3 km/hr, so the time taken to cover this half is: Time = Distance / Speed = (x/2) / 3 = x/6 The total time taken to cover the entire distance is the sum of the times taken to cover each half : Total Time = x/12 + x/6 To add these fractions, we need a common denominator, which is 12. So we can rewrite the fractions as: Total Time = x/12 + 2x/12 = 3x/12 = x/4 Now, we can find the average speed: Average Speed = Total Distance / Total Time = x / (x/4) = 4 km/hr So, the correct answer is: 4 km/hr

Explanation
Let the present age of the baby be x. After 20 years, the baby's age will be x + 20. According to the problem, the baby's age after 20 years will be 5 times the present age , so we can set up the equation: x + 20 = 5x Subtract x from both sides: 20 = 4x Divide both sides by 4: 5 = x So, the present age of the baby is 5 years.

Explanation
Total marks of 28 students in Mathematics = 28 x 50 = 1400 New number of students = 28 - 8 = 20 New average of marks in Mathematics = 50 + 5 = 55 ∴ Total marks of 20 students in Mathematics = 20 x 55 = 1100 ∴ Total marks of 8 students who left the school = 1400 - 1100 = 300 ∴ Average marks of these 8 students =  300/8 = 37.5

Explanation
For one digit number 1 to 9 →1 × 9 = 9 For two digit number 10 to 99 → 2 × 90 = 180 For three digit number 100 to 300 →3 × 201 = 603 Hence, total number of required digits = 9 + 180 + 603  =  792

Explanation

Explanation
A complete day i.e 24 hours is 100%. 24 hours = 24 × 60 minutes = 1440 mins 4 hours, 30 mins = 270 mins 1440 mins = 100% of the day 270 mins = ? = 270 × 100 / 1440 = 18.75% 4 hours and 30 minutes is 18.75% of a day.

Explanation
Total age of new players = Total age of replaced players - Total decrease in age of all players  Total age of new players = 17 + 20 - (11 × 2)/12 ⇒ Total age of new players = 37 - (11/6) ⇒ Total age of new players = (222 - 11)/6 ⇒ Total age of new players = 211/6 ⇒ The Average age of two new players = 211/12 ∴ The average age of two new players is 17 years 7 months.

Explanation
The result of the expression 4 3 − 4 2 2 2 4^3 - frac{4^2}{2^2} ​ is 60. ​

Explanation
Paid= 3/5 Remaining = 1 – 3/5 = 2/5 Given conditions : 2/5 x Total amount = 400 ⇒        Total amount = 1000

Explanation
Let the two numbers be x and y. Given: x + y = 2490 ... (Equation 1) Also, 6.5% of x = 8.5% of y To simplify, convert percentages to decimals : 0.065x = 0.085y Now, divide both sides by 0.065: x = (0.085/0.065)y x = (85/65)y x = (17/13)y ... (Equation 2) Now, substitute Equation 2 into Equation 1: (17/13)y + y = 2490 Combine like terms: (30/13)y = 2490 Multiply both sides by 13/30: y = 1079 Now that we have found y, we can find x: x = 2490 - y (from Equation 1) x = 2490 - 1079 x = 1411 So, the correct answer is: 1411, 1079

Explanation
Let the total distance be x km . The man covers half the distance at 6 km/hr, so the time taken to cover this half is: Time = Distance / Speed = (x/2) / 6 = x/12 The man covers the remaining half at 3 km/hr, so the time taken to cover this half is: Time = Distance / Speed = (x/2) / 3 = x/6 The total time taken to cover the entire distance is the sum of the times taken to cover each half : Total Time = x/12 + x/6 To add these fractions, we need a common denominator, which is 12. So we can rewrite the fractions as: Total Time = x/12 + 2x/12 = 3x/12 = x/4 Now, we can find the average speed: Average Speed = Total Distance / Total Time = x / (x/4) = 4 km/hr So, the correct answer is: 4 km/hr

Explanation
Let the present age of the baby be x. After 20 years, the baby's age will be x + 20. According to the problem, the baby's age after 20 years will be 5 times the present age , so we can set up the equation: x + 20 = 5x Subtract x from both sides: 20 = 4x Divide both sides by 4: 5 = x So, the present age of the baby is 5 years.