Explanation

Total work = Number of labourers x Total days  

Total work = 20 x 8 = 160 units  

Work done in first 4 days = 20 labourers x 4 days  

Work done = 80 units  

Fraction of work completed = Work done / Total work  

= 80 / 160  

= 1 / 2  

Verified & Updated

Explanation

Work (in worker-days) = 15 × 12 = 180

Days for 10 workers = 180 ÷ 10 = 18 days.

Verified & Updated

Explanation

Total number of students = 45  

Ali's rank from the top = 12th  

To find rank from the bottom we use this formula:  

Rank from bottom = Total students - Rank from top + 1  

Put the values:  

Rank from bottom = 45 - 12 + 1  

Rank from bottom = 33 + 1  

Rank from bottom = 34  

Verified & Updated

Explanation

Let sister’s age = x, Sara’s age = 2x

x + 2x = 36 → 3x = 36 → x = 12 → Sara’s age = 24 years.

Verified & Updated

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

Verified & Updated

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  

Verified & Updated

Explanation

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

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

Verified & Updated

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.

Verified & Updated

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.

Verified & Updated

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.

Verified & Updated