Part I Exercise 1.5
Q1. The cost of a car is ₹5,68,345 and a motor bike is ₹2,87,169. Find the total cost of the car and the motor bike.
Sol:
Cost of a car = ₹5,68,345
Cost of a motor bike = ₹2,87,169
Total cost = Cost of car + Cost of motor bike
Total cost = 5,68,345 + 2,87,169
5,68,345
+ 2,87,169
__________
8,55,514
Ans: The total cost of the car and the motor bike is ₹8,55,514.
Q2. In an election, 49,89,65,129 votes were casted. There were only 2 parties, Lok Jan party and Samaj Sevak party. Lok Jan party got 27,19,50,468 votes. How many votes did the Samaj Sevak party get? Who won the election?
Sol:
Total votes casted = 49,89,65,129
Votes obtained by Lok Jan party = 27,19,50,468
Votes obtained by Samaj Sevak party = Total votes – Votes of Lok Jan party
Votes of Samaj Sevak party = 49,89,65,129 – 27,19,50,468
49,89,65,129
– 27,19,50,468
_____________
22,70,14,661
Now, comparing the votes of both parties:
Votes of Lok Jan party (27,19,50,468) > Votes of Samaj Sevak party (22,70,14,661)
Ans: The Samaj Sevak party got 22,70,14,661 votes, and the Lok Jan party won the election.
Q3. A sack of rice weighs 79 kg. What is the weight of 482 such sacks of rice?
Sol:
Weight of one sack of rice = 79 kg
Total number of sacks = 482
Total weight = Weight of one sack × Total number of sacks
Total weight = 482 × 79
482
× 79
_______
4338
+ 33740
_______
38,078
Ans: The total weight of 482 sacks of rice is 38,078 kg.
Q4. Amara has a bakery. She made 55,625 cookies. She has some boxes, in which she is going to pack these cookies. If each box can contain 25 cookies. How many boxes does she need to pack all the cookies?
Sol:
Total number of cookies made = 55,625
Number of cookies in each box = 25
Number of boxes required = Total cookies ÷ Cookies per box
Number of boxes required = 55,625 ÷ 25
25 ) 55625 ( 2225
-50
____
56
-50
____
62
-50
____
125
-125
____
0
Ans: She needs 2,225 boxes to pack all the cookies.
Q5. Jeevan bought two different flavours of toffees. One pack of orange toffees costs ₹35 and one pack of mango toffees costs the same. If he bought 1183 packs of orange toffees and 1817 packs of mango toffees, find the total cost of all the packs of toffees.
Sol:
Cost of one pack of orange toffee = ₹35
Cost of one pack of mango toffee = ₹35
Number of orange toffee packs = 1,183
Number of mango toffee packs = 1,817
Using Distributive Property of Multiplication:
Total Cost = (Cost × Orange packs) + (Cost × Mango packs)
Total Cost = 35 × 1,183 + 35 × 1,817
Total Cost = 35 × (1,183 + 1,817)
Total Cost = 35 × 3,000
Total Cost = 1,05,000
Ans: The total cost of all the packs of toffees is ₹1,05,000.
Q6. A company made 1945 bronze nails, 2493 aluminium nails and 3193 iron nails. Estimate the total number of nails made by the company. (Estimation to nearest hundreds)
Sol:
Rounding off the number of nails to the nearest hundreds:
• Number of bronze nails = 1,945 → Estimated to 1,900 (Tens digit 4 < 5)
• Number of aluminium nails = 2,493 → Estimated to 2,500 (Tens digit 9 > 5)
• Number of iron nails = 3,193 → Estimated to 3,200 (Tens digit 9 > 5)
Total Estimated Nails = 1,900 + 2,500 + 3,200 = 7,600
Ans: The estimated total number of nails made by the company is 7,600.
Q7. A company made a profit of ₹6,89,310. It decided to distribute some of the profit among the top 15 performers of the company. If each person got ₹32,187. How much profit is left with the company?
Sol:
Total profit made by the company = ₹6,89,310
Number of top performers = 15
Amount given to each person = ₹32,187
Total profit distributed = 32,187 × 15
32,187
× 15
_________
160935
+ 321870
_________
4,82,805 (Distributed profit)
Profit left with the company = Total profit – Distributed profit
Profit left = 6,89,310 – 4,82,805
6,89,310
– 4,82,805
_________
2,06,505
Ans: The profit left with the company is ₹2,06,505.
Q8. A cricket stadium is visited by 51,893 people on the first day, 37,890 people on the second day and 42,105 people on the third day. Find the estimated number of people who visited the stadium on all three days. (Estimation to nearest thousands)
Sol:
Rounding off the number of visitors to the nearest thousands:
• Number of people on Day 1 = 51,893 → Estimated to 52,000 (Hundreds digit 8 > 5)
• Number of people on Day 2 = 37,890 → Estimated to 38,000 (Hundreds digit 8 > 5)
• Number of people on Day 3 = 42,105 → Estimated to 42,000 (Hundreds digit 1 < 5)
Total Estimated People = 52,000 + 38,000 + 42,000 = 1,32,000
Ans: The estimated number of people who visited the stadium on all three days is 1,32,000.
Q9. Ayushman has read the numbers wrong and made a mistake in multiplication. He multiplied, 23,54,167 × 34. The actual numbers were, 23,54,167 × 43. Can you find the difference in Ayushman’s answer and actual answer? Can you find the answer without doing multiplication twice?
Sol:
Yes, we can find the answer without multiplying twice by using the Distributive Property:
Given Number = 23,54,167
Actual Multiplication = 23,54,167 × 43
Ayushman’s Multiplication = 23,54,167 × 34
Difference = (23,54,167 × 43) – (23,54,167 × 34)= 23,54,167×9 = 2,11,87,503.
Q10. A company made 2,98,356 tube lights in the month of March and 2,00,568 tube lights in the month of April. If 35,982 tube lights are faulty, find the total number of tube lights which are in good condition.
Sol:
Tube lights manufactured in March = 2,98,356
Tube lights manufactured in April = 2,00,568
First, we find the total production by adding both months:
Total tube lights produced = 2,98,356 + 2,00,568
2,98,356
+ 2,00,568
_________
4,98,924 (Total Production)
Now, given that some tube lights are faulty:
Number of faulty tube lights = 35,982
To find the tube lights in good condition, we subtract the faulty ones from the total production:
Tube lights in good condition = 4,98,924 – 35,982
4,98,924
– 35,982
_________
4,62,942
Ans: The total number of tube lights which are in good condition is 4,62,942.