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NCERT Solutions for Class 5th Maths Chapter 5 Shirts, cloth for bags, a sari border and a new road — Multiplying and Dividing Lengths

Book page 66–67 Updated on2026-09-19

Q1.
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

36 m of cloth is needed.

We need cloth for 20 shirts, and each shirt takes the same amount. So we multiply.

  1. Break the length into its two parts: 1 m and 80 cm.
  2. Multiply each part by 20. 20 × 1 m = 20 m. 20 × 80 cm = 1,600 cm.
  3. Change the centimetres into metres. 1,600 cm = 1,600 ÷ 100 = 16 m.
  4. Add the two answers. 20 m + 16 m = 36 m.
20 × 1 m 80 cm
= (20 × 1 m) + (20 × 80 cm)
= 20 m + 1,600 cm
= 20 m + 16 m
= 36 m of cloth

The other way — change into centimetres first.

1 m 80 cm = 180 cm
20 × 180 = 3,600 cm
3,600 cm = 3,600 ÷ 100 = 36 m ✓ same answer
Why breaking the length up is allowed: Twenty shirts each needing 1 metre plus 80 centimetres is the same as twenty whole metres plus twenty lots of 80 centimetres. You are only grouping the cloth differently — the total does not change.
Check it yourself: Go backwards. 36 m ÷ 20 = 3,600 cm ÷ 20 = 180 cm = 1 m 80 cm, which is exactly one shirt ✓
Q2.
A shop sells cloth for making bags at ₹100 for 5 m. How much money is needed to buy a 1 m cloth? Now, use the double number line to find the cost of the cloth or the length of cloth that we can buy at a particular cost. (Top line: 5 m, 10 m, 20 m, 40 m, ___ m. Bottom line: ₹100, ₹___, ₹___, ₹___, ₹2000. Boxes: ×__, ×__, ×__.)
5 m10 m20 m40 m____ m₹100₹____₹____₹____₹2000× ___× ___× ___
The double number line printed on page 67.
Answer

1 m of cloth costs ₹20.

5 m costs ₹100
1 m costs 100 ÷ 5 = ₹20

Now fill the double number line. Every metre costs ₹20, so to go from the top line to the bottom line you multiply by 20.

5 m10 m20 m 40 m100 m ₹100₹200₹400 ₹800₹2000 ×20 ×2 ×2
Metres on top, rupees below. Down the arrow is ×20; across the top from 5 m to 10 m is ×2.
Length of cloth5 m10 m20 m40 m100 m
Cost₹100₹200₹400₹800₹2000
10 m: 10 × 20 = ₹200
20 m: 20 × 20 = ₹400
40 m: 40 × 20 = ₹800
₹2000: 2000 ÷ 20 = 100 m

The three empty boxes are ×2 (5 m to 10 m), ×20 (metres to rupees) and ×2 (₹100 to ₹200).
Why the two lines move together: Double the cloth, double the money. From 5 m to 10 m the length doubles, and from ₹100 to ₹200 the money doubles too. That is why one arrow labelled ×2 works for both lines.
Check it yourself: 100 m × ₹20 = ₹2,000 ✓ And ₹800 ÷ ₹20 = 40 m ✓
Q3.
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 ₹50. How much money will be needed to buy the thread?
Answer

She needs 10 m of thread, and it will cost ₹500.

Name the quantities first. Every 50 cm of border eats up 1 m of thread. The border is 5 m long.

  1. Put the border into centimetres. 5 m = 5 × 100 = 500 cm.
  2. Find how many 50 cm pieces are in the border. 500 ÷ 50 = 10 pieces.
  3. Each piece needs 1 m of thread. So 10 pieces need 10 × 1 m = 10 m of thread.
  4. Now the money. 1 m of thread costs ₹50, so 10 m cost 10 × 50 = ₹500.
Border = 5 m = 500 cm
500 ÷ 50 = 10 parts
Thread needed = 10 × 1 m = 10 m
Cost = 10 × ₹50 = ₹500
The 5 m border, cut into ten 50 cm pieces each piece = 50 cm Each piece needs 1 m of thread → 10 pieces need 10 m of thread 10 m of thread × ₹50 for each metre = ₹500
Ten equal pieces of border, and one metre of thread for each of them.
Why the thread is longer than the border: Embroidery thread goes up and down through the cloth again and again, so it uses more thread than the plain length of the border. Here it uses twice as much — 1 m of thread for every 50 cm of border.
Check it yourself: If 50 cm needs 1 m, then 1 m of border needs 2 m of thread. So 5 m of border needs 5 × 2 = 10 m ✓ Same answer by a second route.
Q4.
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

2 km 100 m of road is laid each day.

The whole road is shared equally over 6 days, so we divide.

  1. Change the road into metres. 12 km 600 m = 12,000 + 600 = 12,600 m.
  2. Divide by the number of days. 12,600 ÷ 6 = 2,100 m.
  3. Change the answer back. 2,100 m = 2,000 + 100 = 2 km 100 m.
12 km 600 m = 12,600 m
12,600 ÷ 6 = 2,100 m
2,100 m = 2 km 100 m each day

You can also divide the two parts separately, since both split neatly by 6.

12 km ÷ 6 = 2 km
600 m ÷ 6 = 100 m
Together: 2 km 100 m ✓
Why changing to metres is the safe way: The second method only works because both 12 and 600 divide exactly by 6. If the road were 13 km 600 m, 13 would not divide by 6 and the shortcut would break. Changing everything into metres always works.
Check it yourself: 6 days × 2 km 100 m = 12 km 600 m ✓ The whole road is finished, with nothing left over.
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