Explanation

Average of a , b = ( a + b ) /2

16a + 16b = 48

a + b = 3  || divide each term by 16

The average is ( a + b ) / 2 = 3/2

= 1.5

Explanation

Identify the given values: The sum of observations is Sum=1500

. The number of observations is n=30 

Average = Sum of observations / Number of observations

= 1500 / 30

= 50

Explanation

Explanation

If 15 men can complete the work in 12 days,

it means that the total number of man-days required to complete the work is:

15 men * 12 days = 180 man-days.

180 man-days / 9 men = 20 days.

Explanation

If 80 people complete the bridge in 20 days, then the total man-days required to complete the bridge is 80 people * 20 days = 1600 man-days.

Rounding up to the nearest whole number, 70 people will take approximately 23 days to complete the bridge

Explanation

Total students = 27

Since 7 more girls than boys, let's represent the number of boys as x.

Number of girls = x + 7

Total students = Boys + Girls

27 = x + (x + 7)

Combine like terms:

27 = 2x + 7

Subtract 7:

20 = 2x

Divide by 2:

10 = x

Number of boys = 10

Number of girls = 10 + 7 = 17

Therefore:

Total girls in the class = 17

Explanation

Average weight of 16 boys = (50.25 × 16 + 45.15 × 8) / 16 + 8

= 804 + 361.20 / 24

= 1165.20 / 24

= 48.55 kg.

Explanation

Total time taken: T=2t

Average speed = d/t = 230t = 115 km/hr

Explanation

Total students = 26

Students who like football = 21

Students who like cricket = 14

Let x be the number of students who like both football and cricket.

Using the formula:

(Football ∪ Cricket) = Football + Cricket – Both

So,

26 = 21 + 14 – x

26 = 35 – x

x = 35 – 26

x = 9

Explanation

To find how many more men are needed, we can use the formula for work:

$$text{Work} = text{Men} times text{Days}$$

Initially, 120 men can complete the work in 90 days. The total work can be represented as:

$$120 times 90 = 10800 text{ man-days}$$

Now, we need to find how many men are needed to complete the work in 40 days:

$$text{Required Men} = frac{10800}{40} = 270 text{ men}$$