Explanation

Given:

- Present average age of 5 members = 26 years  

→ Total present age = 26 × 5 = 130 years

- Youngest member's present age = 10 years  

→ So, at the time of their birth, 10 years ago:

All other 4 members were each 10 years younger  

→ Total age 10 years ago = 130 – (10 + 10×4) = 130 – 50 = 80 years

→ Number of members at that time = 4 (youngest not born yet)

Average age at that time = 80 ÷ 4 = 20 years

Explanation

4, 9, 20, 43, 90, ?

We already figured out the pattern:

- 9 – 4 = 5  

- 20 – 9 = 11  

- 43 – 20 = 23  

- 90 – 43 = 47

Now, add next difference: 47 + 48 = 95  

→ Next number = 90 + 95 = 185

So the full series is:

4, 9, 20, 43, 90, 185

Explanation

If the average of 20 numbers is zero, their total sum is zero.  

To maximize the number of values greater than zero,  

→ assume only one value is negative,  

→ and the sum of the 19 positive numbers is exactly cancelled by that one negative number.

So, at most 19 numbers can be greater than zero. 

Explanation

The average of the first n natural numbers is:

Average = (n + 1) / 2

For the first 20 natural numbers:  

Average = (20 + 1) / 2 = 21 / 2 = 10.5

Explanation

(x + x²) / 2 = 5x

Multiply both sides by 2:

x + x² = 10x  

x² - 9x = 0  

x(x - 9) = 0  

So, x = 0 or x = 9  

Explanation

Given:

- 5 years ago, average age of A, B, C, and D = 45 years  

- So, total age of A, B, C, and D 5 years ago = 45 × 4 = 180 years  

- Now, their total age = 180 + (5 × 4) = 200 years

- Current average of A, B, C, D, E = 49 years  

- So, total age of all five = 49 × 5 = 245 years

Now, age of E = 245 − 200 = 45 years

Explanation

Given:

- Upstream speed = 60 km/h  

- Downstream speed = 80 km/h  

Let:  

- Speed of boat in still water = x km/h  

- Speed of stream = y km/h  

Formulas:  

- Upstream speed = x - y = 60  

- Downstream speed = x + y = 80  

Add the two equations:  

(x - y) + (x + y) = 60 + 80  

2x = 140  

x = 70 km/h (speed of boat in still water)  

Find y:  

x + y = 80  

70 + y = 80  

y = 10 km/h (speed of stream)  

Explanation

Let:  

- Speed of man in still water = x km/h  

- Speed of stream = y km/h

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Formulas:

- Downstream speed = x + y = 18  

- Upstream speed = x - y = 10  

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Adding both equations:

(x + y) + (x - y) = 18 + 10  

2x = 28  

x = 14 km/h (speed of man in still water)

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Finding y:

x + y = 18  

14 + y = 18  

y = 4 km/h (speed of stream)

Explanation

Given:

- Average marks of all students = 39  

- Scores of 4 students = 5, 12, 15, 19  

- New average after removing these 4 students = 44  

- Number of students = ? (Let it be N)

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Step 1: Calculate total marks of all students

Total marks = Average × Number of students = 39 × N

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Step 2: Calculate total marks of 4 students

Sum of marks of 4 students = 5 + 12 + 15 + 19 = 51

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Step 3: Calculate total marks of remaining students

Total marks after removing 4 students = 44 × (N - 4)

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Step 4: Equation

Total marks of all students - marks of 4 students = total marks of remaining students

=> 39N - 51 = 44 (N - 4)

=> 39N - 51 = 44N - 176

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Step 5: Solve for N

44N - 39N = 176 - 51  

5N = 125  

N = 125 / 5 = 25

Explanation

 80% of 40:  

= (80/100) × 40  

= 0.8 × 40  

= 32

2. 4/5 of 25:  

= (4/5) × 25  

= 20

3. Difference:  

32 − 20 = 12