Explanation

⇒  Let total examines is x.

⇒  65% of total examines has passed. 

⇒  student failed =100%−65%=35%

Then, 35% of examines have failed.

⇒  Number of failures is 420

∴  35% of x=420

∴   35x/100 = 420

 x=(420 * 100)/35

∴  x=1200

Thus, Total number of examines are 1200.

Explanation

• 30% of 100 = 30
• 3% of 1000 = 3/100 × 1000 = 30
• So, 30% of 100 is equal to 3% of 1000.

Explanation

Total percent increase=Initial populationFinal population−Initial population​×100

Increased in 10 years =262,500 − 175,000 =87,500

Increase% = 87,500 / 175,000×100 =50

Average percent increase=

Explanation

To find the average, we need to add the numbers and divide by the total count of numbers.

First, let's add the numbers:

0 + 0 + 4 + 10 + 5 + 5 = 24

There are 6 numbers in the list. To find the average, divide the sum by 6:

24 ÷ 6 = 4

So, the average is 4.

Explanation

Find how many man-days to complete the road:

70*35 = 2450 man-days

Let d = days required for 40 men to do it.

40d = 2450

d=402450​=61.25

Explanation

Given Data:

• 15 men can manufacture 27 baskets in 1 hour (60 minutes).
• We need to find how many baskets 45 men can manufacture in 40 minutes.

Step 1: Baskets manufactured by 1 man in 1 minute

In 1 hour (60 minutes), 15 men manufacture 27 baskets.

Therefore, the number of baskets manufactured by 1 man in 1 minute is:

27 baskets/15 men×60 minutes​ =2/900

$$=0.03\text{ baskets per man per minute}.$$

Step 2: Baskets manufactured by 45 men in 40 minutes

If 1 man manufactures 0.03 baskets per minute, then 45 men will manufacture in 40 minutes:

$$45\times 40\times 0.03=54\text{ baskets}.$$

Explanation

You’re talking about one class.

There are 95 students in the class.

You’re presenting  with two statements

80% of the class failed in Chemistry

30% of the class failed in English

Logic "It means both boys and girls in the class failed, no matter whether they failed in chemistry or English"

Explanation

The formula is A * b / A + B

= 12 * 24 / 12 + 24

= 288 / 36

= 8

Explanation

• Avg of 6 numbers = 30
• Sum of 6 numbers = 6 x 30 = 180
• Avg of first 4 numbers = 25
• Sum of first 4 numbers = 4 x 25 = 100
• Avg of last 3 numbers = 35
• Sum of last 3 numbers = 3 x 35 = 105
• Now, let's find the 4th number:
• Sum of first 3 numbers = Sum of first 4 numbers - 4th number
• = 100 - 4th number
• Sum of first 3 numbers = Sum of all 6 numbers - Sum of last 3 numbers
• = 180 - 105
• = 75
• So, 75 = 100 - 4th number
• 4th number = 100 - 75
• = 25

Explanation

To find the average, we need to first convert each fraction to a decimal:

 5/6 = 0.83

 4/3 = 1.33

 3/4 = 0.75

Then, add the decimals and divide by the number of values:

 0.83 + 1.33 + 0.75 = 2.91

 2.91 ÷ 3 = 0.97

Now, convert the average back to a fraction:

 0.97 ≈ 35/36