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NCERT Solutions for Class 5th Maths Chapter 8 Two balances, one in kilograms and one in grams — Different Units but Same Measure

Book page 105 Updated on2026-09-19

Q1.
Bags are weighed on two different weighing balances. One weighing balance displays weight in kilograms and other displays weight in grams. Match the bags that have the same weights. Weighing Balance 1: 5 kg, 10 kg, 3 kg, 6 kg, 25 kg, 30 kg. Weighing Balance 2: 3,000 g, 6,000 g, 10,000 g, 30,000 g, 5,000 g, 25,000 g.
Answer

Every kilogram weight matches the gram weight that is 1,000 times bigger. The two bags in the picture show it: one balance says 2 kg and the other says 2000 g — and it is the same bag.

  1. Remember the rule: 1 kg = 1,000 g.
  2. Take a weight from Balance 1 and multiply it by 1,000.
  3. Look for that number in Balance 2 and join them.
Weighing Balance 1Multiply by 1,000Weighing Balance 2
5 kg5 × 1,0005,000 g
10 kg10 × 1,00010,000 g
3 kg3 × 1,0003,000 g
6 kg6 × 1,0006,000 g
25 kg25 × 1,00025,000 g
30 kg30 × 1,00030,000 g
Why it happens: The bag does not change. Only the unit changes. A gram is a small unit, so it takes many grams to make the same weight — exactly one thousand of them for every kilogram. Small unit, big number. Big unit, small number.
Check it yourself: Look at the last three digits. Every gram number here ends in three zeros. Cover those three zeros with your finger and the kilogram number is left. 25,000 g → 25 kg.
Q2.
You can use the double number line given below. Complete it.
1 kg3 kg8 kg____ kg20 kg____ kg30 kg1,000 g____ g____ g15,000 g____ g25,000 g____ g×3×1000×___
The double number line printed on page 105. The top line is in kilograms and the bottom line is in grams. Fill in every blank, and the missing number in × ___ .
Answer

Here is the finished double number line. Each kilogram mark on top sits exactly above its gram mark below.

1 kg3 kg8 kg 15 kg20 kg 25 kg30 kg 1,000 g3,000 g8,000 g 15,000 g20,000 g 25,000 g30,000 g Top line: kilograms    Bottom line: grams    (× 1,000 going down) 1 kg → 3 kg is × 3, so 1,000 g → 3,000 g is also × 3
Whatever you do to the top number, do the same to the bottom number.
Top line (kg): 1, 3, 8, 15, 20, 25, 30
Bottom line (g): 1,000; 3,000; 8,000; 15,000; 20,000; 25,000; 30,000

The missing multiplier is × 3
1 kg × 3 = 3 kg, and 1,000 g × 3 = 3,000 g
  1. Blank on top above 15,000 g: 15,000 ÷ 1,000 = 15 kg.
  2. Blank on top above 25,000 g: 25,000 ÷ 1,000 = 25 kg.
  3. Blanks below 3 kg, 8 kg, 20 kg, 30 kg: multiply each by 1,000 → 3,000 g, 8,000 g, 20,000 g, 30,000 g.
  4. The ×___ arrow at the bottom: it goes from 1,000 g to 3,000 g, and 1,000 × 3 = 3,000. So the missing number is 3 — the same as the ×3 arrow on top.
Why it happens: The two lines are locked together. Going down from kg to g you always multiply by 1,000. Going along the line you multiply by whatever you like — but you must do it on both lines, otherwise the two amounts would stop being equal.
Q3.
Notice the relationship between kg and g.
Answer

1 kilogram = 1,000 grams. That one line is the whole relationship.

  1. To go from kg to g, multiply by 1,000. Say it as: add three zeros.
  2. To go from g to kg, divide by 1,000. Say it as: take away three zeros.
7 kg = 7 × 1,000 = 7,000 g
7,000 g = 7,000 ÷ 1,000 = 7 kg
Why it happens: A gram is a very tiny weight — about the weight of one grain of a big rice. You need a thousand of them before you have one kilogram. So the same bag has a small number when you count in kg and a big number when you count in g.
Remember this pair: 1,000 g = 1 kg is the twin of 1,000 mg = 1 g and of 1,000 ml = 1 l. The number 1,000 comes back again and again in this chapter.
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