Standard Units of Measurement

The standard unit of length is metre. 

The standard unit of mass is kilogram (kg). 

The standard unit of capacity is litre (L).

There exist smaller as well as bigger units of length, mass and capacity. 

Their relation are as follows :

1.0Length and Mass of Unit

2.0Solved Examples

1. A vessel has 14 litres 400mL of fruit juice. In how many glasses each of capacity 36 mL can it be filled?

Solution

Since 14 litres 400 mL = 14400 mL

So, number of glasses that can be filled = $\frac{14400}{36}$ = 400 

2. Rohan buys 82 m of fabric to make flags for his favourite cricket team. Each flag will be made using 50 cm of fabric. How many flags can Rohan make?

Solution

Since, 1 m = 100 cm

Then, 82 m = 8200cm

So, number of flags Rohan can make = $\frac{8200}{50}$ = 164

3. There is 528 litres and 260 millilitres of water in the tank. 218 litres and 134 millilitres of water is consumed. How much water is left in the tank? 

Solution

Total capacity of tank = 528 litres and 260 millilitres = 528260 ml

Quantity of water consumed = 218 litres and 134 millilitres = 218134 ml

Quantity of water left in the tank = 528260 – 218134

= 310126 ml or 310 litres and 126 millilitres

4. An auto started its journey and reached different places with a speed of 20 km/hour. The journey is shown below.

(i) Find the total distance covered by the auto from A to D. 

(ii) Find the total distance covered by the auto from D to G.

(iii) Find the total distance covered by the auto, if it starts from A and returns back to A.

(iv) Find the difference of distances from C to D and D to E?

(v) Find out the time taken by the auto to reach

(a) A to B

(b) C to D

(c) E to G

(d) Total journey

Solution

(i) Total distance covered by the auto from A to D 

= 4180 + 3650 + 2360 

= 10,190 km

(ii) Total distance covered by the auto from D to G

= 8250 + 4930 + 2610 = 15790 km

(iii) Total distance = 4180 + 3650 + 2360 + 8250 + 4930 + 2610 + 1120 

= 27100 km

(iv) Difference of distances from C to D and D to E

= 8250 – 2360 = 5890 km

(v)(a) $\frac{4180}{20}=209\text{hrs}$

(b) $\frac{2360}{20}=118\text{hrs}$

(c) $\frac{4930+2610}{20}=377\text{hrs}$

(d) $\frac{\text{Total distance}}{\text{speed}}=\frac{27100}{20}=1355\text{hrs}$

5. What must be added to 34,52,629 to make it equal to 6 crores?

Solution

6 crores = 6,00,00,000

∴ Required number = 6,00,00,000 – 34,52,629 = 5,65,47,371

6. There are 785 students on roll in a residential public school. If the annual fee per student is Rs. 62,606. What is the total fee collected annually by the school.

Solution

Annual fee of one student = Rs. 62,606

Number of students = 785

Total Annual collection of fee = Rs. 62,606 × 785 = Rs. 4,91,45,710

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