Maharashtra Board Class 5 Maths Part Two Chapter 11 Problems on Measurement PDF Download

11. Problems On Measurement

We use the units metre, gram and litre every day to measure length, mass and capacity respectively. While shopping, we use the units rupees and paise. We use units like days, hours and minutes to measure time. Let us see how to carry out basic operations like addition, subtraction, multiplication and division using these units of measurement.

Example (1) Add.

37 km 250 m + 15 km 950 m

250 + 950 = 1200

1200 m = 1 km + 200 m

53 km 200 m

Example (2) Subtract.

7 l 150 ml – 2 l 500 ml

We cannot subtract 500 ml from 150 ml. Convert 1 l into 1000 ml.

4 l 650 ml

Teacher's Note

When we add or subtract measurements, we write them in two columns like rupees and paise. When shopping in India, your mother does this with money every day!

Exam Trick

Remember: When you cannot subtract smaller units, borrow from the bigger unit. Just like borrowing 10 rupees from your father when you have only paise!

Points to Remember

Always write units in two columns - bigger unit and smaller unit.
If you cannot subtract the smaller unit, borrow 1 from the bigger unit.
When adding, if smaller units become bigger, convert them.
1 metre = 100 cm, 1 litre = 1000 ml, 1 kg = 1000 grams.

Problem Set 46

1. Add :

(1) ₹ 9, 50 paise + ₹ 14, 60 paise

(2) 6 cm 5 mm + 7 cm 9 mm

(3) 22 m 50 cm + 25 m 75 cm

(4) 15 km 740 m + 13 km 950 m

(5) 25 kg 650 g + 29 kg 770 g

(6) 19 l 840 ml + 25 l 250 ml

2. Subtract :

(1) ₹ 19, 50 paise - ₹ 12, 60 paise

(2) 24 cm 2 mm - 3 cm 8 mm

(3) 20 m 30 cm - 17 m 60 cm

(4) 40 km 255 m - 17 km 960 m

(5) 35 kg 150 g - 26 kg 470 g

(6) 46 l 200 ml - 38 l 750 ml

Word Problems

Study the following examples.

Example (1) If a shopkeeper has 150 kg 500 g of rice and sells 75 kg 750 g, how much rice will be left?

74 kg 750 g of rice is left.

Teacher's Note

In India, shopkeepers use these methods every day when selling vegetables and rice. Understanding this helps you check if the shopkeeper gave you the correct amount!

Exam Trick

Remember: When you cannot subtract grams, borrow 1 kg which becomes 1000 grams. This is just like borrowing 1 rupee to get 100 paise in money!

Points to Remember

Always write bigger units on the left and smaller units on the right.
Borrow from bigger units when needed for subtraction.
Check your answer by adding the answer back to the smaller amount.
Real shopkeepers in India use this method daily.

Example (2) A can of milk has 20 l 450 ml of milk. Another can has 18 l 800 ml. How much milk is there in the two cans altogether?

The total quantity of milk is 39 l 250 ml.

Example (3) At a speed of 90 km per hour, what distance will a train cover in two and a half hours?

The speed of the train is 90 kmph. That is, it travels 90 km in one hour. It travels 90 more km in the second hour.

In the next half an hour, 90 ÷ 2 = 45 km

The total distance travelled is 90 + 90 + 45 = 225 km.

Teacher's Note

When a train travels at 90 km per hour, it means it goes 90 km in 60 minutes. Indian Railways use this speed calculation every day for all trains!

Exam Trick

Remember: Multiply the speed by the time to find distance. If a train goes 90 km in 1 hour, then in 2 hours it goes 90 × 2 = 180 km.

Points to Remember

Speed = distance covered in 1 hour or 1 minute.
Distance = speed × time.
If time is in half hours or quarter hours, divide the distance by 2 or 4.
Always check if the answer is sensible.

Example (4) If one dress requires 3 m 25 cm of cloth, how much do 4 dresses need?

Manju's method:

3 m 25 cm for the 1st dress

+ 3 m 25 cm for the 2nd dress

+ 3 m 25 cm for the 3rd dress

+ 3 m 25 cm for the 4th dress

1 m is 100 cm, therefore 12 + 1 = 13 m

Kunal's method:

12 m 100 cm = 13 m

Teacher's Note

Tailors in India measure cloth like this when making many clothes. They multiply the cloth needed for one dress by the number of dresses.

Exam Trick

Remember: Use multiplication when the same measurement is repeated. It is faster than adding 4 times!

Points to Remember

Multiply the smaller measurement first, then the bigger measurement.
If smaller units add up to more, convert them to bigger units.
Both methods (adding and multiplying) give the same answer.
Multiplication is faster than adding many times.

Example (5) If a wire that is 9 m 50 cm long is cut into pieces of 5 cm each, how many pieces will be made?

9 m 50 cm = (900 + 50) cm

To find out how many pieces of 5 cm can be made from a wire 950 cm long, let us use division.

190 pieces will be made.

Teacher's Note

In factories in India, workers cut long wires and cloth into smaller pieces every day. Division helps them find how many pieces they can make.

Exam Trick

Remember: Division means splitting something into equal parts. If you want to know how many 5 cm pieces fit in 950 cm, divide 950 by 5.

Points to Remember

Always convert bigger units to smaller units before dividing.
The answer tells you how many equal pieces you can make.
Check: multiply the answer by the piece size to get the total.
If there is a remainder, it means some material is left over.

Example (6) A play started at 30 minutes past 6 in the evening and finished two and three quarter hours later. What time did the play get over?

75 min = 60 min + 15 min

= 1 hr + 15 min

8 hr + 1 hr 15 min = 9 hr 15 min

The play got over at 15 minutes past 9 at night.

Teacher's Note

School plays and movies in India are timed like this. School time tables also use this method to calculate when classes end.

Exam Trick

Remember: Time works differently. 60 minutes = 1 hour. So if minutes add up to more than 60, convert the extra minutes into hours.

Points to Remember

Write hours in one column and minutes in another column.
60 minutes = 1 hour, so borrow and convert like this.
Time is not decimal like meters and grams, so it needs careful conversion.
Always check if your answer makes sense (hours should be between 1 and 12 on a clock).

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