Far and Near — NCERT Solutions

We convert all measurements to the same unit (cm) before comparing.

(a) 456 cm ___ 5 m

Convert 5 m to cm: $5 \text{ m} = 5 \times 100 = 500 \text{ cm}$

Compare: $456 \text{ cm}$ vs $500 \text{ cm}$

$$456 < 500$$

$$\boxed{456 \text{ cm} < 5 \text{ m}}$$

(b) 55 cm + 200 cm ___ 200 cm + 54 cm

Left side: $55 + 200 = 255 \text{ cm}$

Right side: $200 + 54 = 254 \text{ cm}$

Compare: $255$ vs $254$

$$\boxed{55 \text{ cm} + 200 \text{ cm} > 200 \text{ cm} + 54 \text{ cm}}$$

(c) 6 m 5 cm ___ 6 m 50 cm

Convert both to cm:

• $6 \text{ m } 5 \text{ cm} = 600 + 5 = 605 \text{ cm}$
• $6 \text{ m } 50 \text{ cm} = 600 + 50 = 650 \text{ cm}$

Compare: $605$ vs $650$

$$\boxed{6 \text{ m } 5 \text{ cm} < 6 \text{ m } 50 \text{ cm}}$$

(d) 2 m 150 cm ___ 3 m 50 cm

Convert both to cm:

• $2 \text{ m } 150 \text{ cm} = 200 + 150 = 350 \text{ cm}$
• $3 \text{ m } 50 \text{ cm} = 300 + 50 = 350 \text{ cm}$

Compare: $350$ vs $350$

$$\boxed{2 \text{ m } 150 \text{ cm} = 3 \text{ m } 50 \text{ cm}}$$

(e) 238 cm ___ 138 cm + 1 m

Right side: $138 \text{ cm} + 1 \text{ m} = 138 + 100 = 238 \text{ cm}$

Compare: $238$ vs $238$

$$\boxed{238 \text{ cm} = 138 \text{ cm} + 1 \text{ m}}$$

Note: This question refers to a figure/table of statue heights that is not fully visible in the OCR. The standard data used in NCERT Class 5 for this question is:

• Statue of Unity (India): 182 m
• Spring Temple Buddha (China): 128 m
• Statue of Liberty (USA): 93 m
• Christ the Redeemer (Brazil): 38 m
• Motherland Calls (Russia): 85 m

The tallest statue in the world (as per the textbook context) is the Statue of Unity at 182 m.

(a) Difference between the tallest statue (Statue of Unity) and the Statue of Liberty:

$$182 \text{ m} - 93 \text{ m} = 89 \text{ m}$$

The difference is 89 m.

(b) Statues whose heights have the least difference:

Compare all pairs:

• Motherland Calls (85 m) and Statue of Liberty (93 m): $93 - 85 = 8$ m
• Spring Temple Buddha (128 m) and Statue of Unity (182 m): $182 - 128 = 54$ m

The least difference is between the Motherland Calls and the Statue of Liberty (difference = 8 m).

(c) Statues whose heights have the largest difference:

The largest difference is between the tallest and the shortest statues:

• Statue of Unity (182 m) and Christ the Redeemer (38 m): $182 - 38 = 144$ m

The largest difference is between the Statue of Unity and Christ the Redeemer (difference = 144 m).

(d) Height of which statue doubled equals the Statue of Unity (182 m)?

We need: $2 \times h = 182$

$$h = 182 \div 2 = 91 \text{ m}$$

The statue closest to 91 m is the Statue of Liberty (93 m). Based on the textbook data, the answer is the Statue of Liberty (approximately, depending on exact figures given in the figure).

Given: $1 \text{ km} = 1{,}000 \text{ m}$

Number of ropes needed $= 1{,}000 \div \text{length of each rope}$

Given: Total race distance $= 3 \text{ km} = 3{,}000 \text{ m}$

Water stations are placed every $500 \text{ m}$.

Number of water stations $= 3{,}000 \div 500 = 6$

However, a water station at the finish line (3,000 m) may not be needed as a separate station. Based on standard interpretation, stations are placed after the start and before or at the finish:

Positions from the starting point:
$$500 \text{ m},\ 1{,}000 \text{ m},\ 1{,}500 \text{ m},\ 2{,}000 \text{ m},\ 2{,}500 \text{ m},\ 3{,}000 \text{ m}$$

Number of water stations = 6

They will be placed at: 500 m, 1,000 m, 1,500 m, 2,000 m, 2,500 m, and 3,000 m from the starting point.

Given: Total race distance $= 3 \text{ km} = 3{,}000 \text{ m}$

Children stand at every $300 \text{ m}$.

Number of positions $= 3{,}000 \div 300 = 10$

Positions from the starting point:
$$300 \text{ m},\ 600 \text{ m},\ 900 \text{ m},\ 1{,}200 \text{ m},\ 1{,}500 \text{ m},\ 1{,}800 \text{ m},\ 2{,}100 \text{ m},\ 2{,}400 \text{ m},\ 2{,}700 \text{ m},\ 3{,}000 \text{ m}$$

Number of children needed = 10

They will stand at: 300 m, 600 m, 900 m, 1,200 m, 1,500 m, 1,800 m, 2,100 m, 2,400 m, 2,700 m, and 3,000 m from the starting point.

Given: Total race distance $= 3 \text{ km} = 3{,}000 \text{ m}$

Flags are placed every $50 \text{ m}$.

Total number of flag positions (not counting the start) $= 3{,}000 \div 50 = 60$

Flags are placed alternately (Red, Blue, Red, Blue, …) starting from the first position at 50 m.

Total flags = 60

Since flags alternate:

• Red flags = $60 \div 2 = 30$
• Blue flags = $60 \div 2 = 30$

30 red flags and 30 blue flags are needed till the finish line.

Note: The specific sub-questions for this table are not fully visible in the OCR. Below are the key facts that can be derived from the table, which are typically asked:

Total distance of the journey (Dibrugarh to Kanniyakumari):
$$= 4{,}187 \text{ km}$$

Distance between consecutive stations (for reference):

• Dibrugarh to Dimapur: $306 \text{ km}$
• Dimapur to Guwahati: $556 - 306 = 250 \text{ km}$
• Guwahati to Jalpaiguri Road: $983 - 556 = 427 \text{ km}$
• Jalpaiguri Road to Bhubaneswar: $2{,}007 - 983 = 1{,}024 \text{ km}$
• Bhubaneswar to Visakhapatnam: $2{,}450 - 2{,}007 = 443 \text{ km}$
• Visakhapatnam to Vijayawada JN: $2{,}800 - 2{,}450 = 350 \text{ km}$
• Vijayawada JN to Coimbatore JN: $3{,}675 - 2{,}800 = 875 \text{ km}$
• Coimbatore JN to Kanniyakumari: $4{,}187 - 3{,}675 = 512 \text{ km}$

Students should use the table to answer specific questions about distances between stations as directed by the teacher.

Concept used: $10 \text{ mm} = 1 \text{ cm}$

Convert each length to mm for ease of measurement:

1. $5 \text{ cm } 5 \text{ mm} = 50 + 5 = 55 \text{ mm}$
2. $3 \text{ cm } 6 \text{ mm} = 30 + 6 = 36 \text{ mm}$
3. $8 \text{ cm } 3 \text{ mm} = 80 + 3 = 83 \text{ mm}$
4. $36 \text{ mm} = 3 \text{ cm } 6 \text{ mm}$
5. $67 \text{ mm} = 6 \text{ cm } 7 \text{ mm}$

Steps to draw each line:

• Place the scale on the notebook.
• Mark the starting point at 0.
• Mark the ending point at the required length.
• Join the two points with a sharp pencil to draw the line.

How to draw 36 mm and 67 mm lines:

For 36 mm: Since most scales show both cm and mm markings, place the scale and mark from 0 to the 36 mm mark (which is the same as 3 cm 6 mm mark). Draw the line.

For 67 mm: Mark from 0 to the 67 mm mark (which is the same as 6 cm 7 mm). Draw the line.

Alternatively, if the scale only shows cm, convert: $36 \text{ mm} = 3.6 \text{ cm}$ and $67 \text{ mm} = 6.7 \text{ cm}$, and mark accordingly between the cm markings.

Relationships used:
$$10 \text{ mm} = 1 \text{ cm}, \quad 100 \text{ cm} = 1 \text{ m}, \quad 1{,}000 \text{ m} = 1 \text{ km}$$

mm ↔ cm number line:
For every 1 cm, there are 10 mm.

• 1 cm = 10 mm
• 2 cm = 20 mm
• 5 cm = 50 mm
• 10 cm = 100 mm

cm ↔ m number line:
For every 1 m, there are 100 cm.

• 1 m = 100 cm
• 2 m = 200 cm
• 5 m = 500 cm
• 10 m = 1,000 cm

m ↔ km number line:
For every 1 km, there are 1,000 m.

• 1 km = 1,000 m
• 2 km = 2,000 m
• 5 km = 5,000 m

(Students should fill in the blanks on the number lines in their textbook using the above relationships.)