Explanation

Work done by 12 men in 4 days = 1 (full work)

Work done by 1 man in 4 days = 1/12

Work done by 6 men in 4 days = 6/12 = 1/2 (i.e., half of the work)

Work done by 6 men in 2 days = (1/2) × (2/4) = 1/4

Remaining work = 1 - 1/4 = 3/4

15 women complete the full work in 4 days → 1 woman’s 1-day work = 1/(15 × 4) = 1/60

Work needed in 3 days → x women × 3 × (1/60) = 3/4

x = (3/4) × (60/3) = 15 women

Explanation

Let's calculate:

Regular wages for 40 hours = 40 * Rs. 30 = Rs. 1200

Total wages received = Rs. 1680

Overtime wages = Rs. 1680 - Rs. 1200 = Rs. 480

Overtime wage rate = 2 * Rs. 30 = Rs. 60/hour

Number of overtime hours = Overtime wages / Overtime wage rate

= Rs. 480 / Rs. 60

= 8 hours

Explanation

Given:

• 16 machines finish the work in 4 days

• Now we want to know how many days will take 8 machines for the same work

Concept:

More machines → Less time
Fewer machines → More time
This is an inverse proportion relationship.

So,

$$text{Days} propto frac{1}{text{Machines}}$$ $$text{New Days} = 4 times frac{16}{8} = 4 times 2 = 8 text{ days}$$

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

Convert the speed of the train from km/hr to m/s:

45 km/hr = 45 × 1000 m / 3600 s = 12.5 m/s

The train crosses the bridge in 30 seconds, so the total distance covered is the length of the train plus the length of the bridge. Let's call the length of the bridge "x". Then, the total distance = 130 m (train length) + x.

Since the train crosses the bridge in 30 seconds, we can use the formula:

Distance = Speed × Time

Substitute the values:

130 m + x = 12.5 m/s × 30 s

Simplify the equation:

130 m + x = 375 m

Subtract 130 m from both sides:

x = 245 m

So, the length of the bridge is 245 m.

Explanation

To find the speed of the car, we need to divide the distance traveled (700 km) by the time taken (3 hours 30 minutes).

First, let's convert the time from hours and minutes to just hours:

3 hours 30 minutes = 3.5 hours (converting 30 minutes to 0.5 hours)

Now, let's calculate the speed:

Speed = Distance ÷ Time = 700 km ÷ 3.5 hours = 200 km/h

So, the correct answer is:

200 km/h

Explanation

To find the required speed, we first calculate the distance covered by the train:

$$text{Distance} = text{Speed} times text{Time} = 45 , text{km/h} times 5 , text{hours} = 225 , text{km}$$

Now, to cover this 225 km in 3 hours, the required speed is:

$$$$Speed=Distance/Time=225 km/3 hours=75 km/h

Explanation

 Given:

6 men × 8 hours/day = total man-hours per day = 48 man-hours

They earn Rs. 720 per week

Now:

8 men × 6 hours/day = 48 man-hours per day — same total man-hours as before

So, since the total man-hours per day (and thus per week) are the same, the weekly earnings will also be the same.

Explanation

To solve this, we need to find how much distance B covers in the time it takes A to finish the race.

• A's time: 36 seconds to cover 100 meters
• B's time: 45 seconds to cover 100 meters

First, we calculate B's speed:

• B's speed = Distance / Time = 100 m / 45 sec = 2.22 m/sec

Now, in 36 seconds (the time A takes to finish the race), B will cover:

• Distance covered by B = B's speed × A's time = 2.22 m/sec × 36 sec = 80 m

Since A finishes the race in 36 seconds, but B only covers 80 meters, A beats B by 100 - 80 = 20 meters.

Explanation

Speed = 120 km/hour

Distance = Speed × Time = 120 × 8 = 960 km