Explanation

Father is 36 years older than son. 

So father's present age = x + 36 years

After 6 years:

Son's age = x + 6 years

Father's age = x + 36 + 6 = x + 42 years

Given: In 6 years, father's age will be 3 times the age of his son.

So, x + 42 = 3 * (x + 6)

Solve the equation:

x + 42 = 3x + 18

42 - 18 = 3x - x

24 = 2x

x = 12

Son's present age = 12 years

Father's present age = x + 36 = 12 + 36 = 48 years

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Explanation

Given:  

15 workers complete the work in 20 days  

Step 1: Find total work  

Total work = Number of workers x Number of days  

Total work = 15 x 20 = 300  

Step 2: Find workers needed for 10 days  

Let the required number of workers = W  

W x 10 = 300  

W = 300 / 10  

W = 30  

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Explanation

The word SPEECH has 6 letters, with E repeated twice.

Number of arrangements = 6! ÷ 2! = 720 ÷ 2 = 360.

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Explanation

A's rate = 1/6, B's rate = 1/4; together = 5/12 of the work per hour.

In 2 hours, they complete 10/12 = 5/6 of the work, leaving 1/6.

A alone completes 1/6 of the work in 1 hour.

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Explanation

For a round table we use (n-1)! to arrange people.  

First arrange the 3 men around the table. This can be done in (3-1)! = 2! = 2 ways.  

When 3 men are seated they create 3 places between them. Since each women must sit between 2 men, the 3 women will sit in these 3 places.  

The 3 women can be arranged in these places in 3! = 6 ways.  

Therefore total number of ways = 2 × 6 = 12 ways.

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Explanation

Floor changes: 10 → 9 → 11 → 8 → 12 → 7 → 13

Net change = −1 + 2 − 3 + 4 − 5 + 6 = +3

Starting from the 10th floor, the elevator reaches the 13th floor.

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Explanation

The number of circular arrangements of n distinct people is (n − 1)!

For 5 children: (5 − 1)! = 4! = 24

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Explanation

Each office has 8 seats.

To fit 34 people:

34 ÷ 8 = 4 offices with 32 seats, and you’ll still need 2 more seats.

So you need 5 offices.

4 offices = 32 seats  

5 offices = 40 seats → enough for all 34 people

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Explanation

15 men × 20 days = 300 man-days (total work)

Now, with 25 men:

300 man-days ÷ 25 men = 12 days

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Explanation

Let son's present age = x years

Then father's present age = x + 24 years

After 2 years:

Son's age = x + 2

Father's age = x + 24 + 2 = x + 26

Given, After 2 years father's age = 2 _ son's age

So, x + 26 = 2 _ (x + 2)

x + 26 = 2x + 4

26 - 4 = 2x - x

22 = x

Son's present age = 22 years

Father's present age = x + 24 = 22 + 24 = 46 years

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