We appreciate your visit to 1 If 12 men can cut a lawn in 3 days in how many days can 4 men cut the same lawn if they work. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Sure! Let's break down each problem and explain how we can find the answers step-by-step:
1) If 12 men can cut a lawn in 3 days, in how many days can 4 men cut the same lawn if they work at the same rate?
- First, we calculate the total amount of work required, which is equivalent to the number of men (12) multiplied by the number of days (3) they work, resulting in [tex]\(12 \times 3 = 36\)[/tex] man-days.
- To find out how many days it will take 4 men to complete the same work, we divide the total man-days by the number of men: [tex]\(\frac{36}{4} = 9\)[/tex] days.
2) The ratio of cement and sand in a mortar is 5:2. If the cement is 25kg, what is the weight of the sand?
- The total ratio of cement to sand is [tex]\(5 + 2 = 7\)[/tex] parts.
- If the cement represents 5 parts, we can find 1 part by dividing the cement weight by its number of parts: [tex]\(\frac{25 \, \text{kg}}{5} = 5 \, \text{kg per part}\)[/tex].
- Since sand is 2 parts, the sand's weight is [tex]\(2 \times 5 \, \text{kg} = 10 \, \text{kg}\)[/tex].
3) If 12 men can dig a trench in 8 days, how many men can dig it in 6 days at the same rate?
- The total work is [tex]\(12 \times 8 = 96\)[/tex] man-days.
- To find out how many men are required to complete the job in 6 days, we divide the total man-days by the number of days: [tex]\(\frac{96}{6} = 16\)[/tex] men.
4) If 6 men do a piece of work in 3 days, how many men will be needed to do it in 2 days?
- The total work is [tex]\(6 \times 3 = 18\)[/tex] man-days.
- To find the number of men needed to complete the work in 2 days, we use: [tex]\(\frac{18}{2} = 9\)[/tex] men.
5) A student reads an average of 5 pages of a book per day. How many pages did he read in 3 weeks?
- There are 7 days in a week, so in 3 weeks, there are [tex]\(3 \times 7 = 21\)[/tex] days.
- The total pages read are [tex]\(5 \times 21 = 105\)[/tex] pages.
6) A plot of ground can be ploughed by 7 ploughs in 21 days. How long will 5 of the same machines take to plough twice as much ground?
- Ploughing twice as much ground would require double the work, which is [tex]\(7 \times 21 \times 2 = 294\)[/tex] plough-days.
- With 5 ploughs, the time taken is [tex]\(\frac{294}{5} = 58.8\)[/tex] days.
7) A bridge is to be constructed by 120 men in 180 days. If the bridge is to be completed in 150 days, how many more men are required?
- The total work is [tex]\(120 \times 180 = 21600\)[/tex] man-days.
- To complete the work in 150 days, the number of men needed is [tex]\(\frac{21600}{150} = 144\)[/tex].
- The additional men required: [tex]\(144 - 120 = 24\)[/tex] men.
8) If 330 men are required to construct a 30 km track of railway in 9 months, how long will it take 275 men, working at the same rate, to construct 150 km of track?
- The total work for 30 km is [tex]\(330 \times 9 = 2970\)[/tex] man-months.
- To find out how long it takes 275 men to construct 150 km, we establish work proportionality: set up the ratios, solve to find [tex]\(\frac{150 \times 275}{2970} \approx 13.89\)[/tex] months.
9) A boy is 5 times as old as a girl. If their total age is 48 years, how old is the girl?
- Let the girl's age be [tex]\(x\)[/tex]. Then the boy's age is [tex]\(5x\)[/tex].
- The equation is [tex]\(x + 5x = 48\)[/tex], which simplifies to [tex]\(6x = 48\)[/tex].
- Solving for [tex]\(x\)[/tex], the girl's age is [tex]\(x = \frac{48}{6} = 8\)[/tex] years.
I hope this explanation is clear and helps you understand each solution!
1) If 12 men can cut a lawn in 3 days, in how many days can 4 men cut the same lawn if they work at the same rate?
- First, we calculate the total amount of work required, which is equivalent to the number of men (12) multiplied by the number of days (3) they work, resulting in [tex]\(12 \times 3 = 36\)[/tex] man-days.
- To find out how many days it will take 4 men to complete the same work, we divide the total man-days by the number of men: [tex]\(\frac{36}{4} = 9\)[/tex] days.
2) The ratio of cement and sand in a mortar is 5:2. If the cement is 25kg, what is the weight of the sand?
- The total ratio of cement to sand is [tex]\(5 + 2 = 7\)[/tex] parts.
- If the cement represents 5 parts, we can find 1 part by dividing the cement weight by its number of parts: [tex]\(\frac{25 \, \text{kg}}{5} = 5 \, \text{kg per part}\)[/tex].
- Since sand is 2 parts, the sand's weight is [tex]\(2 \times 5 \, \text{kg} = 10 \, \text{kg}\)[/tex].
3) If 12 men can dig a trench in 8 days, how many men can dig it in 6 days at the same rate?
- The total work is [tex]\(12 \times 8 = 96\)[/tex] man-days.
- To find out how many men are required to complete the job in 6 days, we divide the total man-days by the number of days: [tex]\(\frac{96}{6} = 16\)[/tex] men.
4) If 6 men do a piece of work in 3 days, how many men will be needed to do it in 2 days?
- The total work is [tex]\(6 \times 3 = 18\)[/tex] man-days.
- To find the number of men needed to complete the work in 2 days, we use: [tex]\(\frac{18}{2} = 9\)[/tex] men.
5) A student reads an average of 5 pages of a book per day. How many pages did he read in 3 weeks?
- There are 7 days in a week, so in 3 weeks, there are [tex]\(3 \times 7 = 21\)[/tex] days.
- The total pages read are [tex]\(5 \times 21 = 105\)[/tex] pages.
6) A plot of ground can be ploughed by 7 ploughs in 21 days. How long will 5 of the same machines take to plough twice as much ground?
- Ploughing twice as much ground would require double the work, which is [tex]\(7 \times 21 \times 2 = 294\)[/tex] plough-days.
- With 5 ploughs, the time taken is [tex]\(\frac{294}{5} = 58.8\)[/tex] days.
7) A bridge is to be constructed by 120 men in 180 days. If the bridge is to be completed in 150 days, how many more men are required?
- The total work is [tex]\(120 \times 180 = 21600\)[/tex] man-days.
- To complete the work in 150 days, the number of men needed is [tex]\(\frac{21600}{150} = 144\)[/tex].
- The additional men required: [tex]\(144 - 120 = 24\)[/tex] men.
8) If 330 men are required to construct a 30 km track of railway in 9 months, how long will it take 275 men, working at the same rate, to construct 150 km of track?
- The total work for 30 km is [tex]\(330 \times 9 = 2970\)[/tex] man-months.
- To find out how long it takes 275 men to construct 150 km, we establish work proportionality: set up the ratios, solve to find [tex]\(\frac{150 \times 275}{2970} \approx 13.89\)[/tex] months.
9) A boy is 5 times as old as a girl. If their total age is 48 years, how old is the girl?
- Let the girl's age be [tex]\(x\)[/tex]. Then the boy's age is [tex]\(5x\)[/tex].
- The equation is [tex]\(x + 5x = 48\)[/tex], which simplifies to [tex]\(6x = 48\)[/tex].
- Solving for [tex]\(x\)[/tex], the girl's age is [tex]\(x = \frac{48}{6} = 8\)[/tex] years.
I hope this explanation is clear and helps you understand each solution!
Thanks for taking the time to read 1 If 12 men can cut a lawn in 3 days in how many days can 4 men cut the same lawn if they work. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
