Explanation

Given Information:

• A lifter loads 200 packages per hour.
• A labor loads two quarters (i.e., 2/4 or 1/2) less than 200 packages per hour.
  • 1​/2×200=100
  • So, the labor loads 200 - 100 = 100 packages per hour.
• Together, the lifter and labor load:
  $$200+100=300\text{ packages per hour}$$
• They need to load 1500 packages.
• They take 30 minutes (0.5 hours) rest after every 2 hours of loading.

Step 1: Calculate Total Loading Time Without Breaks

1500/300​=5 hours

So, if they were working continuously, they would need exactly 5 hours.

Step 2: Account for Breaks

• They work for 2 hours, then take a 30-minute (0.5-hour) break.
• In 2 hours, they load:
  $$2\times 300=600\text{ packages}$$
• After 2 hours, they take a 0.5-hour break.
• Continuing this cycle:
  • First 2 hours: 600 packages (then a 30-minute break)
  • Next 2 hours: 600 packages (then a 30-minute break)
  • Remaining: 300 packages, which takes 1 more hour (no need for another break).

Total time including breaks:

$$2+0.5+2+0.5+1=5.5\text{ hours}$$

Step 3: Select the Correct Answer

$$(\mathbf{b})5.5\text{ hours}$$

Explanation

Let:

• M1 = Number of machines in the first case = 8
• D1 = Number of days taken in the first case = 10
• M2 = Number of machines in the second case = 16
• D2 = Number of days taken in the second case =?

The formula for inverse proportion is: M1 * D1 = M2 * D2

Substitute the values: 8 * 10 = 16 * D2 80 = 16 * D2

To find D2, divide both sides by 16: D2 = 80 / 16 D2 = 5

So, it will take 16 machines 5 days to do the work.

Explanation

 1 hour = 820 jumps

30 minutes = (820 ÷ 2) = 410 jumps

Explanation

 To calculate the duration between 21:30 (9:30 PM) and 7:30 (7:30 AM), follow these steps:

Convert to 24-Hour Format:

Departure: 21:30

Arrival: 07:30 (next day)

Calculate Duration:

From 21:30 to midnight (00:00): 2 hours 30 minutes

From midnight to 07:30: 7 hours 30 minutes

Total duration: 2:30 + 7:30 = 10 hours

Therefore, the correct answer is B. 10 Hours.

Explanation

Meena's problem-solving rate per minute:
24 problems ÷ 15 minutes = 1.6 problems per minute

In 40 minutes:
1.6 × 40 = 64 problems.

Explanation

To find speed, convert the time to hours and distance to kilometers:

Time = 2 minutes 30 seconds = 2.5 minutes = 2.5/60 = 1/24 hours

Distance = 750 meters = 0.75 kilometers

Speed = Distance / Time = 0.75 / (1/24) = 0.75 x 24 = 18 km/hr

Explanation

If A completes a work in 1 day, B completes the same work in 3 days

Hence, if the difference is 2 days, B can complete the work in 3 days

=> if the difference is 60 days, B can complete the work in 90 days

=> Amount of work B can do in 1 day= 1/90

Amount of work A can do in 1 day = 3 × (1/90) = 1/30

Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45

=> A and B together can do the work in 45/2 days = 22 ½ days

Explanation

Explanation

Step 1: Use the Diagonal Formula for a Square

For a square with side length $s$, the diagonal $d$ is given by:

Substituting $d = 30$

$sqrt{2} approx 1.414$

Step 3: Calculate the Perimeter

The perimeter $P$ of a square is:

Explanation

  (50 / 2) - 15 = 10 cm width