RBSE Solutions Class 5 Maths Chapter 15 Capacity Exercise 15.1

Capacity Ex 15.1

Question 1. Radha pours out 3 water containers of 500 ml., 200 ml. and 100 ml. respectively into a thermos. Now the thermos is exactly half filled. Find the capacity of thermos.
Answer: Radha combined water from three containers into a thermos. The quantities were 500 ml, 200 ml, and 100 ml. After pouring these, the thermos was exactly half full. We need to find the total capacity of the thermos.
First, we calculate the total amount of water Radha poured: \( 500 \text{ ml} + 200 \text{ ml} + 100 \text{ ml} = 800 \text{ ml} \).
Since this 800 ml fills half the thermos, the full capacity of the thermos will be double this amount.
So, the full capacity of the thermos is \( 800 \text{ ml} \times 2 = 1600 \text{ ml} \). Understanding how half-filled capacities relate to total capacity is key in solving these types of problems.
In simple words: Radha put 800 ml of water into a thermos, and it filled half. This means the whole thermos can hold twice that amount, which is 1600 ml.

🎯 Exam Tip: Always make sure to consider if the given volume represents a part or the whole capacity before calculating the total.

Question 2. Capacity of a small can of kerosene is 3 litre. How much amount of kerosene, will be required to fill 8 such cans.
Answer: A small can has a capacity of 3 litres of kerosene. We need to find the total amount of kerosene required to fill 8 such cans.
To find the total amount of kerosene, we multiply the capacity of one can by the number of cans.
Total kerosene needed \( = 3 \text{ litres/can} \times 8 \text{ cans} = 24 \text{ litres} \).
Therefore, 24 litres of kerosene will be needed to fill 8 cans. This is a direct multiplication problem, useful for calculating total quantities based on unit capacity.
In simple words: One can holds 3 litres. To fill 8 cans, you need 8 times 3 litres, which is 24 litres of kerosene.

🎯 Exam Tip: For simple quantity problems, remember to multiply the unit capacity by the number of units required.

Question 3. How many packets of milk having capacity of 250 ml. can be packed from 10 litre amount of milk.
Answer: We have a total of 10 litres of milk, and each packet has a capacity of 250 ml. We need to determine how many packets can be filled from this total amount of milk.
First, we must convert the total amount of milk from litres to millilitres, as the packet capacity is in millilitres: \( 10 \text{ litres} = 10 \times 1000 \text{ ml} = 10,000 \text{ ml} \).
Next, divide the total volume of milk by the capacity of one packet to find the number of packets that can be filled:
Number of packets \( = \frac { 10,000 \text{ ml} }{ 250 \text{ ml} } = 40 \).
So, 40 packets of milk, each holding 250 ml, can be filled from 10 litres of milk. Converting all measurements to the same unit (millilitres in this case) is a crucial first step for accurate calculations.
In simple words: We have 10 litres of milk, which is 10,000 ml. Since each packet holds 250 ml, we divide 10,000 by 250 to find that 40 packets can be filled.

🎯 Exam Tip: Always ensure all quantities are in the same unit (e.g., all ml or all litres) before performing calculations involving different units of measure.

Question 5. Fill in the blanks
(i) 3 containers of capacity.............. can be fully filled from \( 1\frac {1}{2} \) litre of quantity.
(ii) 1 litre of container can be.............. filled by using 500 ml. of container .............. times.
(iii) The price of 2 litre 250 ml. milk is .............. Rs at the rate of 40 Rs per litre.
(iv) How many millilitre are there in 1 litre.
Answer: Let's fill in the blanks using our understanding of capacity and pricing.
(i) \( 1\frac {1}{2} \) litres is equal to 1500 ml. If 3 containers are filled from this quantity, each container will have a capacity of \( 1500 \text{ ml} \div 3 = 500 \text{ ml} \).
(ii) A 1-litre container holds 1000 ml. To fill it using 500 ml containers, we need \( 1000 \text{ ml} \div 500 \text{ ml} = 2 \) times.
(iii) The price of 1 litre is 40 Rs. So, for 2 litres, it's \( 2 \times 40 \text{ Rs.} = 80 \text{ Rs.} \). For 250 ml (which is \( \frac{1}{4} \) of a litre), the cost is \( \frac{1}{4} \times 40 \text{ Rs.} = 10 \text{ Rs.} \). Total price \( = 80 \text{ Rs.} + 10 \text{ Rs.} = 90 \text{ Rs.} \).
(iv) There are \( 1000 \text{ ml} \) in 1 litre.
Understanding unit conversions (litres to millilitres) and basic arithmetic is essential for these types of practical problems.
In simple words: (i) Three containers from 1.5 litres means each is 500 ml. (ii) A 1-litre container needs two 500 ml containers to fill it. (iii) Milk costs 40 Rs per litre, so 2.25 litres would cost 90 Rs. (iv) One litre is the same as 1000 millilitres.

🎯 Exam Tip: For fill-in-the-blanks involving units, always ensure you perform necessary conversions (e.g., litres to millilitres) to get the correct numerical value.

Question 6. A water tank is filled by a tap from above while it is emptied by another tap at the bottom. If the above tap fills with the speed of 25 litre per hour and the bottom tap drains it with the speed of 10 litre per hour. After 4 hours what will be the amount of water left in the tank (imagine initially the tank was empty).
Answer: A water tank has two taps: one that fills it from the top and one that empties it from the bottom. The top tap fills at a rate of 25 litres per hour, and the bottom tap drains at a rate of 10 litres per hour. We need to find out how much water will be in the tank after 4 hours, assuming it starts empty.
First, calculate the net rate at which water accumulates in the tank. This is the filling rate minus the draining rate:
Net filling rate \( = 25 \text{ litres/hour} - 10 \text{ litres/hour} = 15 \text{ litres/hour} \).
This means that for every hour, the tank gains 15 litres of water.
To find the total amount of water after 4 hours, we multiply the net filling rate by the total time:
Total water after 4 hours \( = 15 \text{ litres/hour} \times 4 \text{ hours} = 60 \text{ litres} \).
So, after 4 hours, there will be 60 litres of water in the tank. This is a classic example of a "rate of change" problem where the net effect of multiple actions determines the final quantity.
In simple words: The tank fills by 25 litres and empties by 10 litres every hour, so it gains 15 litres per hour. After 4 hours, it will have \( 15 \times 4 = 60 \) litres of water.

🎯 Exam Tip: When dealing with multiple rates (filling and draining), first calculate the net rate of change to determine the overall effect over time.