We are given a set of multiple-choice math problems, and we need to find the correct answers.

1. Problem Description

We are given a set of multiple-choice math problems, and we need to find the correct answers.

2. Solution Steps

1. A car travelled a distance of 50km in an hour. What distance did it travel in 30 minutes at the same speed?

Since the car travels at a constant speed, the distance traveled is proportional to the time. 30 minutes is half an hour, so the car will travel half the distance in 30 minutes.

$50 \text{ km} / 2 = 25 \text{ km}$.

2. It takes 15 men, 48 days to weed a plot of land. How many men can weed the same plot of land in 16 days, if they work at the same rate?

The amount of work is constant. Let $m$ be the number of men and $d$ the number of days. The total work done is proportional to $m \times d$.

$15 \times 48 = x \times 16$, where $x$ is the number of men.

$x = \frac{15 \times 48}{16} = 15 \times 3 = 45$ men.

3. 8 girls can weed a plot of land in 10 days. How many days will 5 girls to weed the same plot of land, if they work at the same rate?

The amount of work is constant. Let $g$ be the number of girls and $d$ the number of days. The total work done is proportional to $g \times d$.

$8 \times 10 = 5 \times x$, where $x$ is the number of days.

$x = \frac{8 \times 10}{5} = 8 \times 2 = 16$ days.

4. 30 men can dig a pit in 21 days. How many days will 14 men take to dig the pit, working at the same rate?

The amount of work is constant. Let $m$ be the number of men and $d$ the number of days. The total work done is proportional to $m \times d$.

$30 \times 21 = 14 \times x$, where $x$ is the number of days.

$x = \frac{30 \times 21}{14} = 30 \times \frac{3}{2} = 15 \times 3 = 45$ days.

5. A train travels at a speed of 80km per hour. How long will it take to travel a distance of 320km?

Time = Distance / Speed

$t = \frac{320}{80} = 4$ hours.

6. A van travels 154km in $1\frac{3}{4}$ hours. Find its speed in km/h.

Speed = Distance / Time

Time = $1\frac{3}{4} = \frac{7}{4}$ hours

Speed = $\frac{154}{\frac{7}{4}} = \frac{154 \times 4}{7} = 22 \times 4 = 88 \text{ km/h}$

7. It takes 6 students 1 hour to sweep their schools compound. How long will it take 15 students to sweep the same compound?

The amount of work is constant. Let $s$ be the number of students and $t$ the time. The total work done is proportional to $s \times t$.

$6 \times 1 = 15 \times x$, where $x$ is the time in hours.

$x = \frac{6}{15} = \frac{2}{5}$ hours.

$\frac{2}{5} \times 60 \text{ minutes} = 2 \times 12 = 24 \text{ minutes}$

8. A car travelling at 60km per hour. How far does it travel in $2\frac{1}{2}$ hours?

Distance = Speed × Time

Time = $2\frac{1}{2} = \frac{5}{2}$ hours.

Distance = $60 \times \frac{5}{2} = 30 \times 5 = 150 \text{ km}$

9. A watch gains $1\frac{1}{2}$ minutes per hour. What is the total time gained from 12 noon to 12 midnight in a day?

$1\frac{1}{2} = \frac{3}{2}$ minutes per hour. From 12 noon to 12 midnight is 12 hours.

Total gain = $\frac{3}{2} \times 12 = 3 \times 6 = 18$ minutes.

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0. A printing machine prints 600 books in 3 hours. How many books will the machine print in 5 hours?

Books per hour = $\frac{600}{3} = 200$.

In 5 hours, it prints $200 \times 5 = 1000$ books.

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1. A car uses 150 litres of petrol in 45 minutes. How many litres of petrol will it use in 1 hour?

45 minutes = $\frac{3}{4}$ hour.

Rate of petrol usage = $\frac{150}{\frac{3}{4}} = \frac{150 \times 4}{3} = 50 \times 4 = 200$ litres per hour.

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2. If 5 boys took 14 days to cultivate a piece of land, how long will it 7 boys working at the same rate, to cultivate the land?

$5 \times 14 = 7 \times x$, where x is the number of days.

$x = \frac{5 \times 14}{7} = 5 \times 2 = 10$ days.

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3. Fifteen boys took 12 hours to weed a plot of land. If nine boys work at the same rate, how long will it take them to weed the plot of land?

$15 \times 12 = 9 \times x$, where x is the number of hours.

$x = \frac{15 \times 12}{9} = \frac{5 \times 4}{1} = 20$ hours.

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4. Find the simple interest on $28,000.00 at $3\frac{1}{2}$% per annum for 6 months.

$I = PRT$

$P = 28000$, $R = 3.5/100 = 0.035$, $T = 6/12 = 0.5$

$I = 28000 \times 0.035 \times 0.5 = 28000 \times 0.0175 = 490$

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5. Mr. Yevu saved $2,500.00 at a simple interest of 25% per annum for 4 years. Calculate the interest he earned on his savings.

$I = PRT$

$P = 2500$, $R = 0.25$, $T = 4$

$I = 2500 \times 0.25 \times 4 = 2500 \times 1 = 2500$

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6. Find the simple interest on $15,000.00 at a rate of 20% per annum for 5 years.

$I = PRT$

$P = 15000$, $R = 0.20$, $T = 5$

$I = 15000 \times 0.20 \times 5 = 15000 \times 1 = 15000$

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7. Calculate the simple interest on $130,000.00 for $2\frac{1}{2}$ years at 12% per annum.

$I = PRT$

$P = 130000$, $R = 0.12$, $T = 2.5$

$I = 130000 \times 0.12 \times 2.5 = 130000 \times 0.3 = 39000$

3. Final Answer

1. D. 25km

2. D. 45

3. D. 16 days

4. D. 45

5. C. 4 hours

6. B. 88km/h

7. A. 24 minutes

8. D. 150 km

9. C. 18 minutes

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0. B. 1000 books

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1. D. 200 litres

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2. C. 10 days

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3. D. 20 hours

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4. A. $490.00

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5. B. $2,500.00

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6. B. $15,000.00

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7. B. $39,000.00