Explanation

Current total marks = Average * Number of tests

= 60 * 4

= 240

New average = 65

New total tests = 5

New total marks = New average * New total tests

= 65 * 5

= 325

Marks needed in the fifth test = New total marks - Current total marks

= 325 - 240

= 85

Explanation

We are told:

Average of 5 numbers = 34

Total sum of 5 numbers = 34 × 5 = 170

Given 3 numbers: 28, 30, 32

Sum of these = 28 + 30 + 32 = 90

Remaining sum = 170 - 90 = 80

Remaining numbers = 2

Average of remaining = 80 ÷ 2 = 40

Explanation

Let the total number of rabbits = x

Let the total number of pigeons = y

total number of head = 20 

                x + y = 20        eq (1)

total number of feet = 48 

             4x  +2y  = 48

              2x + y   = 24    eq (2)

Subtracting equation (2) from eq (1)

   2x + y -x - y = 24 -20

        x = 4

Explanation

To find when both traffic signals will blink together again, we need to find the Least Common Multiple (LCM) of 8 and 12.

LCM of 8 and 12:

Prime factors of 8 = 2 × 2 × 2

Prime factors of 12 = 2 × 2 × 3

LCM = 2 × 2 × 2 × 3 = 24

Explanation

First and Third Numbers:

9² = 81

8² = 64

So for 10: 10² = 100 → third number is 100

Now the middle number:

9 × 5 = 45

8 × 4.5 = 36

Seems like:

Middle number = First number × 5 (for 9), and × 4.5 (for 8)

Let’s check the pattern:

9 → ×5 = 45

8 → ×4.5 = 36

So 10 → ×4 = 40

Final Set:

10 (40) (100)

Explanation

Total time = 1 hour = 60 minutes

Commercials duration = 20 * 30 seconds

= 600 seconds

= 10 minutes

Percentage of hour taken by commercials = (10/60) * 100

= 16.67%

Nearest percent = 17%

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

Man climbs 20 yards and slips down 5 yards in one minute

i.e. he climbs (20-5 = 15 yards) in one minute.

But in the last minute, he will be climbing 20 yards as he gets on the top so no slip.

Time taken to climb 80 yards = 60/15 + 1

                                                   = 5 minutes.

He climbs the hill in 5 minutes

Explanation

Now, let's examine the differences between consecutive terms:

17 − 6 = 11

39 − 17 = 22

72 − 39 = 33

The pattern of differences: +11, +22, +33 → increasing by 11 each time.

Next difference should be: +44

So,

72 + 44 = 116

Explanation: Differences follow a pattern: +11, +22, +33, +44.

Explanation

Given:

40% of employees didn't go to the meeting, and this equals 28 employees:

40% of x = 28

(40/100)x = 28

0.4x = 28

x = 28 / 0.4

x = 70