NCERT Solutions Class 5 Mathematics Mela Chapter 05 Far and Near

Page 57

Let Us Find

Question. Identify the appropriate units for measuring each of the following.
Answer: Choose the unit based on what you are measuring. For very small things like a pencil or a button, use centimetres (cm) or millimetres (mm). For medium-sized objects like a room or a playground, use metres (m). For very long distances like the space between towns or cities, use kilometres (km).
In simple words: Small objects need small units like cm. Big distances need big units like km.

Exam Tip: Remember that cm and mm work for small items, m works for medium distances, and km works for very long distances.

Page 57

Different Units but Same Measure

Question. Shikha and Sonu are measuring the lengths of saris and stoles in the village weaving centre. Find which measures represent the same sari or stole. You can take help of the double number line below.
Answer: Use the double number line to match measurements in different units. The pairs that represent the same sari or stole are: 204 cm matches 5 metre 40 cm; 540 cm matches 2 metre 204 cm; 750 cm matches 2 metre 4 cm; 240 cm matches 2 metre 40 cm; and 404 cm matches 6 metre 150 cm. Convert each measurement to the same unit to check if they are equal - for example, 204 cm = 2 m 4 cm, and 5 m 40 cm = 540 cm, so these are different.
In simple words: Change all numbers to the same unit, then see which ones are the same length.

Exam Tip: Always convert measurements to a single unit before comparing - either change everything to cm or everything to m and cm.

Page 58

Let Us Compare

Question 1. Ritika is comparing the lengths of different rods. Compare them using <, =, > signs.
(a) 456 cm ____ 5 m
(b) 55 cm + 200 cm ____ 200 cm + 54 cm
(c) 6 m 5 cm ____ 6 m 50 cm
(d) 2 m 150 cm ____ 3 m 50 cm
(e) 238 cm ____ 138 cm + 1 m
Answer:
(a) We know that 5 m = 500 cm. Therefore, 456 cm < 500 cm. So, 456 cm < 5 m.
(b) LHS = 55 + 200 = 255 cm, and RHS = 200 + 54 = 254 cm. Here, 255 cm > 254 cm. Therefore, 55 cm + 200 cm > 200 cm + 54 cm.
(c) LHS = 6 m 5 cm = 605 cm, and RHS = 6 m 50 cm = 650 cm. Here, 605 cm < 650 cm. Therefore, 6 m 5 cm < 6 m 50 cm.
(d) LHS = 2 m 150 cm = 200 cm + 150 cm = 350 cm, and RHS = 3 m 50 cm = 300 cm + 50 cm = 350 cm. Here, 350 cm = 350 cm. Therefore, 2 m 150 cm = 3 m 50 cm.
(e) LHS = 238 cm, and RHS = 138 cm + 1 m = 138 cm + 100 cm = 238 cm. Here, 238 cm = 238 cm. Therefore, 238 cm = 138 cm + 1 m.
In simple words: Turn everything into the same unit before you compare - either all cm or all m. Then use < (less), = (equal), or > (more).

Exam Tip: Always convert mixed units (m and cm) to a single unit before comparing; this prevents errors.

Question 2. Some of World's Tallest Statues
(a) What is the difference between the height of the tallest statue in the world and the Statue of Liberty?
(b) Identify the statues whose heights have the least difference.
(c) Identify the statues whose heights have the largest difference.
(d) The height of which statue will be equal to the height of the Statue of Unity, if it is doubled?
Answer:
(a) Height of Statue of Unity = 183 m, and Height of Statue of Liberty = 93 m. Difference = 183 m - 93 m = 90 m. So, the difference between the height of the tallest statue in the world and the Statue of Liberty is 90 m.
(b) Height of Statue of Liberty = 93 m, and Height of The Motherland Calls = 91 m. Difference = 2 m. These two statues have heights that differ the least.
(c) Tallest statue: Statue of Unity (183 m), and Shortest statue: Christ the Redeemer (38 m). Difference = 183 m - 38 m = 145 m. These two have the largest difference in height.
(d) Height of Statue of Unity = 183 m. We need a statue whose height × 2 = 183 m. So, Height = 183 m ÷ 2 = 91.5 m. Looking at the list, The Motherland Calls has height 91 m, which is very close. (Guanvin is 108 m and 108 × 2 = 216; Spring Buddha is 128 m and 128 × 2 = 256). So, 91 m is the closest. Hence, the height of The Motherland Calls will be equal to the height of the Statue of Unity if it is doubled.
In simple words: Find the difference by subtracting one height from another. The smallest difference shows the closest statues, and the biggest difference shows the most different statues.

Exam Tip: For part (d), always divide by 2 and then find the value closest to that result in the given list.

Page 59

Let Us Do

Question. Measure 100 m and 200 m on your school playground or any other place in and around your school, using a Long Tape. Mark these points and draw a straight line. Walk on the lines and count the number of steps. Use this relationship between the number of steps taken and distance walked to find distances around you for at least 3 locations. Wherever possible, walk and find the number of steps. Otherwise, find the distance and estimate the number of steps.
(a) Identify and write the locations that are the nearest and the farthest from your home.
(b) Write the distances obtained above in increasing order.
(c) Name a location that is equal to or more than 1,000 m from your home.
Answer:
(a) Nearest location: My school playground (about 200 m). Farthest location: Railway station (about 2 km = 2000 m).
(b) Distances in increasing order: Playground - 200 m, Market - 500 m, Park - 800 m, Railway station - 2000 m. So, in order: 200 m, 500 m, 800 m, 2000 m.
(c) The Railway station (2000 m) is more than 1000 m from my home.
In simple words: Walk different distances and write them down. Put them in order from smallest to largest. Find places that are far away - more than 1000 m (1 km).

Exam Tip: For this activity-based question, actual measured distances from your own area are expected - the examiner looks for reasonable estimates and correct ordering skills.

Page 59

Let Us Explore

Understanding Kilometre

When we walk 1,000 m, we say we have walked 1 km. The relationship is: 1,000 m = 1 km. The word "Kilo" stands for thousand. This unit is used to measure long distances.

Page 60

Kilometre Race

Question 1. Sheena and Jennifer are helping to organise a 3-km race. Water stations are to be arranged after every 500 m. How many water stations must be set up? At what positions from the starting point will these water stations be placed?
Answer: To make 1 km of rope we need 1000 m of ropes. For a 3 km race, we need 3000 m of rope. Water stations every 500 m: Number of stations = 3000 m ÷ 500 m = 6 stations. Positions: 500 m, 1000 m, 1500 m, 2000 m, 2500 m, 3000 m.
In simple words: Divide the total distance by the spacing between stations. You get 6 stations placed at these 6 spots along the race.

Exam Tip: Always divide the total distance by the interval to find how many stations you need.

Question 2. Children need to stand at an interval of 300 m to direct the runners. How many children are needed? At what positions from the starting point will the children be standing?
Answer: Children every 300 m: Number of children = 3000 m ÷ 300 m = 10 children. Positions: 300 m, 600 m, 900 m, 1200 m, 1500 m, 1800 m, 2100 m, 2400 m, 2700 m, 3000 m.
In simple words: Divide the total distance by 300 to get 10 children. Place them at the spots shown.

Exam Tip: Count carefully and list all positions - missing even one position costs a mark.

Question 3. Red and blue flags are to be placed alternately at every 50 m. How many red and blue flags are needed till the finish line?
Answer: Flags every 50 m (Red and Blue alternately): Number of flag points = 3000 m ÷ 50 m = 60 points. Since they are alternate (Red, Blue, Red, Blue...), there will be an equal number of each. Number of Red flags = 30. Number of Blue flags = 30.
In simple words: Divide to get 60 spots total. Since you alternate colors, you get 30 of each color.

Exam Tip: When items alternate, the count is split equally between the two types.

Page 60

Let Us Do

Question. The longest train journey in India is by The Vivek Express which runs from Dibrugarh in Assam to Kanniyakumari in Tamil Nadu. Look at the stations on the route shown in the table below and answer the questions.
(1) The total length of the route from Dibrugarh to Kanniyakumari is ____ km.
(2) The distance between Vijayawada and Jalpaiguri road is ____.
(3) Distance between Vijayawada and Visakhapatnam is ____.
(4) Which two stations are farther apart - Guwahati and Dimapur or Bhubaneswar and Jalpaiguri Road?
(5) What is the distance between Guwahati and Coimbatore JN?
Answer:
(1) Total distance mentioned in the table last row (Kanniyakumari) is 4187 km.
(2) Distance between Vijayawada (2,800 km) and Jalpaiguri Road (983 km): Difference = 2800 km - 983 km = 1817 km.
(3) Difference = 2800 km - 2450 km = 350 km.
(4) Distance between Guwahati (556 km) and Dimapur (306 km) = 556 km - 306 km = 250 km. Distance between Bhubaneswar (2007 km) and Jalpaiguri Road (983 km) = 2007 km - 983 km = 1,024 km. So, Bhubaneswar and Jalpaiguri Road are farther apart.
(5) Distance between Coimbatore (3675 km) and Guwahati (556 km) = 3675 km - 556 km = 3119 km.
In simple words: Use the table to find each station's distance from the start. To find the distance between two stations, subtract the smaller distance from the larger one.

Exam Tip: Always subtract the smaller value from the larger to get a positive difference between two stations.

Page 61

Let Us Measure

Question. Measure the lines in the design and write their measurements in cm and mm.
Answer: Side lengths of the figures: ABCD = 10 cm 0 mm, XYZW = 9 cm 0 mm, PQRS = 7 cm 5 mm, EFGH = 5 cm 5 mm. Length and width of Blue boxes: Length = 3 cm, Width = 1 cm. Length and width of Red box: Length = 1 cm 60 mm (or 2 cm 60 mm as written), Width = 90 mm.
In simple words: Place your scale on each line and read the measurement. Write it in cm and mm format.

Exam Tip: Always place the zero end of the scale at the start of the line and read where it ends; note both the cm and mm values.

Page 62

Let Us Do

Question. Soak some seeds of whole moong or black or white chana overnight. Next morning, take them out and wrap them in a moist cloth to sprout them. Over the next 4 days, take out one seed each day and measure the length of sprout. For ease of measurement, you can either place the seed on a paper and mark the length of the sprout, or use a thread to find its length.
Answer:

Exam Tip: This is an observation-based activity - your actual measurements from your seeds may differ, but consistent measurement and recording are what matter.

Question. Let Us Draw - Draw lines of the following lengths in your notebook using a scale.
(1) 5 cm 5 mm
(2) 3 cm 6 mm
(3) 8 cm 3 mm
(4) 36 mm
(5) 67 mm
How did you draw lines of lengths 36 mm and 67 mm? Share your thoughts in class.
Answer:
To draw a line of 36 mm: First, I looked at the scale. On the scale, 1 cm = 10 mm. So, 36 mm means 3 cm and 6 mm. I kept my pencil on 0, then marked a point at 3 cm 6 mm, and joined the two points with a straight line.
To draw a line of 67 mm: Again, I checked the scale. 67 mm = 6 cm and 7 mm. I placed the scale at 0, then marked at 6 cm 7 mm, and drew the line neatly.
My thought: I learned that whenever the number is in mm, I can convert it into cm and mm to make it easy. This way, I don't get confused with big numbers.
In simple words: Turn mm into cm and mm. For example, 36 mm becomes 3 cm 6 mm. Then use your scale to mark and draw.

Exam Tip: Always convert pure millimetre values to cm and mm format before using the scale - it makes reading the scale much easier.

Page 63

Question. Fill in the blanks appropriately in the double number lines given below.
Answer:
(a) The pattern shows multiplying by 7 on the top line and by 10 on the bottom line. Fill in: 28 cm, 32 cm, 45 cm, 50 cm (top); 280 mm, 320 mm, 450 mm, 500 mm (bottom).
(b) The pattern shows multiplying by 4 on the top line and by 100 on the bottom line. Fill in: 12 m, 14 m, 17 m, 21 m (top); 1200 cm, 1400 cm, 1700 cm, 2100 cm (bottom).
(c) The pattern shows multiplying by 9 on the top line and by 1,000 on the bottom line. Fill in: 41 km, 55 km, 67 km, 82 km (top); 41,000 m, 55,000 m, 67,000 m, 82,000 m (bottom).
In simple words: Look at how the numbers change on one line. Apply the same change to the other line to fill in the blanks.

Exam Tip: Always identify the pattern or multiplier first, then use it consistently to fill all blanks.

Question. Use your understanding from above to fill in the blanks appropriately.
(a) 4 cm 5 mm = ____ mm
(b) 89 mm = ____ cm ____ mm
(c) 234 cm = ____ mm
(d) 514 mm = ____ cm ____ mm
(e) 6 m 34 cm = ____ cm
(f) 20 m 12 cm = ____ cm
(g) 397 m = ____ cm
(h) 5,792 cm = ____ m ____ cm
(i) 9,108 cm = ____ m ____ cm
(j) 34 km = ____ m
(k) 6,870 m = ____ km ____ m
(l) 10,552 m = ____ km ____ m
(m) 29 km 30 m = ____ m
(n) 32 km 359 m = ____ m
Answer:
(a) 4 cm 5 mm = 45 mm
(b) 89 mm = 8 cm 9 mm
(c) 234 cm = 2340 mm
(d) 514 mm = 51 cm 4 mm
(e) 6 m 34 cm = 634 cm
(f) 20 m 12 cm = 2012 cm
(g) 397 m = 39700 cm
(h) 5,792 cm = 57 m 92 cm
(i) 9,108 cm = 91 m 8 cm
(j) 34 km = 34000 m
(k) 6,870 m = 6 km 870 m
(l) 10,552 m = 10 km 552 m
(m) 29 km 30 m = 29030 m
(n) 32 km 359 m = 32359 m
In simple words: Use the conversion facts: 1 cm = 10 mm, 1 m = 100 cm, and 1 km = 1000 m. Multiply or divide to change from one unit to another.

Exam Tip: Memorize these key conversions and practise them repeatedly - they form the foundation for all measurement questions.

Question 1. Rani has two red-coloured ribbon rolls, one of length 3 m 75 cm and another 2 m 25 cm long. How much ribbon does she have?
Answer: Rani's first ribbon is 3 m 75 cm long and her second ribbon is 2 m 25 cm long. When you add these together: 3 m 75 cm + 2 m 25 cm = 5 m 100 cm. Since 100 cm equals 1 m, the total length becomes 6 m.
In simple words: Add the two ribbon lengths. When the centimetre part adds up to 100 or more, change it into metres.

Exam Tip: Remember to convert extra centimetres into metres when the total goes beyond 100 cm - this is a key step that examiners check for.

Question 2. The distance from Bhopal to Sanchi is 48 km 700 m. Bhadbhada Ghat waterfall is on the way and 17 km 900 m away from Bhopal. How far is Sanchi from the waterfall?
Answer: The total distance from Bhopal to Sanchi is 48 km 700 m. The waterfall sits 17 km 900 m from Bhopal. To find the distance from the waterfall to Sanchi, convert 48 km 700 m to 47 km 1700 m (since 1 km = 1000 m). Now subtract: 47 km 1700 m - 17 km 900 m = (47 - 17) km + (1700 - 900) m = 30 km 800 m. Therefore, Sanchi is 30 km 800 m away from the waterfall.
In simple words: When you cannot subtract the metres part easily, borrow 1 km from the kilometres part and change it to 1000 metres.

Exam Tip: Always regroup (borrow) when the metres in the second number are bigger than the metres in the first number - this prevents errors in subtraction.

Question 3. Gulmarg Gondola in Gulmarg, Kashmir is the second longest and second highest cable car in the world. It is divided into two sections. The first section covers 2 km 300 m and the second section covers 2 km 650 m. What is the total distance covered by the cable car?
Answer: The first section of the cable car stretches 2 km 300 m. The second section stretches 2 km 650 m. Adding them together: 2 km 300 m + 2 km 650 m = 4 km 950 m. This is the complete distance covered by the cable car.
In simple words: Add up both parts. Since 300 cm and 650 m together make 950 m (less than 1000 m), you do not need to change them into kilometres.

Exam Tip: Check if the total metres are 1000 or more after adding - only then should you convert the extra metres into kilometres.

Question 4. Circle the bigger length and find the difference. (a) 11 mm and 1 cm
Answer: Convert 1 cm to millimetres: 1 cm = 10 mm. Now compare: 11 mm is bigger than 10 mm. The difference is 11 mm - 10 mm = 1 mm.
In simple words: Change both measurements to the same unit before comparing them.

Exam Tip: Always convert to the smaller unit first - this makes comparison and subtraction easier.

Question 4. (b) 26 mm and 2 cm
Answer: Change 2 cm to millimetres: 2 cm = 20 mm. Comparing the two: 26 mm is the bigger measurement. The difference is 26 mm - 20 mm = 6 mm.
In simple words: Convert larger units to smaller ones, then compare and subtract.

Exam Tip: Write both measurements in the same unit on paper before you circle the bigger one - this prevents careless mistakes.

Question 4. (c) 20 cm and 201 mm
Answer: Convert 20 cm to millimetres: 20 cm = 200 mm. Comparing: 201 mm is bigger than 200 mm. The difference is 201 mm - 200 mm = 1 mm.
In simple words: One measurement was almost equal to the other - they differ by just 1 mm.

Exam Tip: When two lengths are very close, double-check your conversion to avoid saying the wrong one is bigger.

Question 4. (d) 1,020 mm and 1 m
Answer: Convert 1 m to millimetres: 1 m = 1000 mm. Comparing: 1020 mm is bigger than 1000 mm. The difference is 1020 mm - 1000 mm = 20 mm.
In simple words: 1 metre equals exactly 1000 millimetres, so 1020 mm is 20 mm longer.

Exam Tip: Remember the key conversions: 1 m = 1000 mm, 1 cm = 10 mm - these are used over and over in length problems.

Question 4. (e) 2 m and 245 cm
Answer: Convert 2 m to centimetres: 2 m = 200 cm. Comparing: 245 cm is bigger than 200 cm. The difference is 245 cm - 200 cm = 45 cm.
In simple words: The second length is 45 cm more than the first.

Exam Tip: After finding the difference, check your answer by adding it back - does 200 cm + 45 cm = 245 cm? If yes, you got it right.

Question 4. (f) 5,678 m and 6 km
Answer: Convert 6 km to metres: 6 km = 6000 m. Comparing: 6000 m is bigger than 5678 m. The difference is 6000 m - 5678 m = 322 m.
In simple words: 6 kilometres is longer than 5678 metres by 322 metres.

Exam Tip: Use the conversion 1 km = 1000 m to turn all distances into the same unit before comparing.

Question 4. (g) 6 km 1,480 m and 7 km 479 m
Answer: Convert both to metres: 6 km 1480 m = 7480 m and 7 km 479 m = 7479 m. Comparing: 7480 m is bigger. The difference is 7480 m - 7479 m = 1 m.
In simple words: These two lengths are almost the same - they differ by just 1 metre.

Exam Tip: When lengths are given in both kilometres and metres, always convert to a single unit to avoid confusion.

Question 5. We need a 1 m 80 cm cloth to make a shirt for a 10-year old child. How much cloth will be needed to make shirts for 20 such children?
Answer: Each shirt requires 1 m 80 cm of cloth. For 20 shirts, multiply: 20 times 1 m 80 cm = (20 times 1 m) plus (20 times 80 cm) = 20 m + 1600 cm. Since 1600 cm = 16 m, the total is 20 m + 16 m = 36 m.
In simple words: Multiply the length of cloth for one shirt by the number of shirts. Then convert the extra centimetres into metres.

Exam Tip: Break down mixed measurements (metres and centimetres) into separate parts before multiplying - this reduces arithmetic errors.

Question 6. A shop sells cloth for making bags at Rs. 100 for 5 m. How much money is needed to buy a 1 m cloth?
Answer: If 5 m of cloth costs Rs. 100, then 1 m of cloth costs Rs. 100 divided by 5, which is Rs. 20. A double number line can help you find the cost of any length of cloth or the length you can buy at any given cost.
In simple words: Divide the total price by the total metres to find the price per metre.

Exam Tip: The double number line is a fast visual way to solve problems where price and length are linked proportionally.

Question 7. Anita is making an embroidery on the border of a sari. She needs a 1 m long thread to embroider a 50 cm sari. How much thread would she need for a 5 m sari border? A 1 m long thread costs Rs. 50. How much money will be needed to buy the thread?
Answer: For a 50 cm sari border, 1 m (or 100 cm) of thread is needed. For each 1 cm of border, the thread required is 100 divided by 50 = 2 cm. For a 5 m (or 500 cm) border, the thread needed is 2 times 500 = 1000 cm, which equals 10 m. Since each metre of thread costs Rs. 50, the cost for 10 m is 10 times Rs. 50 = Rs. 500.
In simple words: First find how much thread is needed per centimetre of border. Then multiply to get the total thread for the whole border. Finally, multiply the metres of thread by the cost per metre.

Exam Tip: Break multi-part questions into smaller steps - find the rate first, then calculate the total amount, then find the total cost.

Question 8. A road 12 km 600 m long is being laid in a town. The workers lay an equal length of road each day, and complete the work in 6 days. How much road-laying work is done on each day?
Answer: The total road length is 12 km 600 m, which equals 12600 m. The work is finished in 6 days, with an equal amount laid each day. Divide the total by the number of days: 12600 m divided by 6 = 2100 m per day. Converting back to mixed form: 2100 m = 2 km 100 m.
In simple words: Change everything to the smaller unit, divide by the number of days, then change the answer back to kilometres and metres if needed.

Exam Tip: Always convert mixed measurements to a single unit before dividing - this makes the arithmetic cleaner and reduces errors.