Important Questions with Solutions: The Dairy Farm | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download

Q1: Estimate the product by rounding to the nearest tens:

1. 128 × 283 = .....................
2. 224 × 314 = .....................
3. 168 × 312 = .....................
4. 183 × 249 = .....................

Sol:

1. Round each number to the nearest tens: 128 rounds to 130
   283 rounds to 280
   Now, multiply the rounded numbers:
   130 × 280 = 36400

2. Round each number to the nearest tens: 224 rounds to 220
   314 rounds to 310
   Now, multiply the rounded numbers:
   220 × 310 = 68200

3. Round each number to the nearest tens: 168 rounds to 170
   312 rounds to 310
   Now, multiply the rounded numbers:
   170 × 310 = 52700

4. Round each number to the nearest tens: 183 rounds to 180
   249 rounds to 250
   Now, multiply the rounded numbers:
   180 × 250 = 45000

Q2: Multiply the following numbers: 652 × 152 = .....................

Sol: Q3: Multiply 487 by 300.

Sol:

Step 1:  Multiply 487 by 3.

Step 2: Insert two zeros on the right of the product to get 1 ,46,100.
Hence, 487 x 300 = 1 ,46, 100.

Q4: Multiply 231 by 4,000.

Sol: Step 1: Multiply 231 by 4.

 
Step 2: Insert three zeros on the right of the product at the end to get 9,24,000.
Hence, 231 x 4,000 = 9,24,000.

Q5: A bag contains 125 kg of rice. How much rice will 89 such bags have?

Sol: Amount of rice in 1 bag = 125 kg.
Amount of rice in 89 bags = 125 x 89 kg

 
Hence, 89 bags will contain 11,1 25 kg rice.

Q6: How many seconds are there in a day? 

Sol: Number of  hours in 1 day = 24

Number of minutes in 1 hour = 60
Number of seconds in 1 minute = 60 

The total number of seconds in 1 day = 24 x (60 x 60) = 24 x 3600 

Q7: Multiply 1,369 by 90.

Sol: Step 1: Multiply 1 ,369 by 9.
Step 2: Insert one zero on the right of the product to get 1,23,210.

 
 Hence, 1,369 x 90 = 1,23,210.

Q8: Multiply 153 by 800.

Sol:

Step 1: Multiply 153 by 8.

Step 2: Insert two zeros on the right of the product to get 1,22,400.
Hence, 153 x 800 = 1,22,400.

Q9: Multiply 105 by 7,000.

Sol: Step 1: Multiply 105 by 7.

Step 2: Insert three zeros on the right of the product to get 7,35,000.

Hence, 105 x 7,000 = 7,35,000.

Q10: 45 students and 6 teachers went on a day trip by train. One ticket per student cost them Rs. 175 and one ticket per teacher cost them Rs. 275. How much money they must have spent on their round trip? 
Sol: 

• S as the number of students (45 students),
• T as the number of teachers (6 teachers),
• C_s as the cost per student ticket (Rs. 175),
• C_t as the cost per teacher ticket (Rs. 275).

The total cost for students (Ts) is given by the formula: T_s=S×C_s

And the total cost for teachers (T_t) is given by the formula: T_t=T×C_t

We can find the total cost (T_total) by adding the total cost for students and the total cost for teachers: T_total=  T_s+T_t

Substitute the given values into the formulas:  T_s = 45 × 175

and T_t = 6×275

T_total = T_s + T_t = 7875 + 1650 = 9525

Therefore, the group must have spent Rs. 9525 on their round trip.

Q10: A bus travels a distance of 285 km every day. What distance will it travel in a year?

Sol: Distance travelled by the bus in one day = 285 km 

There are 365 days in a year. 

Distance travelled by the bus in 365 days = 285 km x 365

Hence, the bus will travel 1,04,025 km in a year

Q11: A laborer can pack 575 apples in one hour and every day he works for 8 hours. How many apples will he pack in the month of February?

Sol: Number of apples collected in 1 hour = 575

Number of hours for which he works in a day = 8

Total number of apples collected in 1 day = 575 x 8 

Number of days in the month of February(considering non leap year) = 28

Therefore, total number of days = 575 x 8 x 28 

Q12: Estimate the product of 325 and 18.

Sol: 325 → 300 (Rounding off to hundred's place)
18 → 20 (Rounding off to ten's place).
325 X 18 → 300 X 20 = 6,000.
Thus, estimated product is 6,000.