Problems 1 - 23 : Evaluate.
Problem 1 :
40 + 30
Problem 2 :
80 + 50
Problem 3 :
46 + 30
Problem 4 :
52 + 34
Problem 5 :
126 + 78
Problem 6 :
208 + 126
Problem 7 :
85 + 49
Problem 8 :
291 + 76
Problem 9 :
70 - 30
Problem 10 :
80 - 50
Problem 11 :
56 - 20
Problem 12 :
84 - 55
Problem 13 :
126 - 78
Problem 14 :
208 - 126
Problem 15 :
16 x 7
Problem 16 :
12 x 25
Problem 17 :
25 x 9
Problem 18 :
8 x 49
Problem 19 :
73 x 6
Problem 20 :
9 x 999
Problem 21 :
8 x 125
Problem 22 :
103 x 9
Problem 23 :
250 x 12
Problem 24 :
498 x 6
Problem 25 :
12 x 18
Problem 26 :
16 x 17
Problem 27 :
18 x 19
Problem 28 :
12 x 13
Problem 29 :
19 x 16
Problem 30 :
10% of 54.32
Problem 31 :
10% of 820
Problem 32 :
20% of 500
Problem 33 :
35% of 900
Problem 34 :
5% of 370
Problem 35 :
3% of 400
Problem 36 :
6% of 450
Problem 37 :
7% of 90
Problem 38 :
Find the simple ineterest on $700 for 3 years at the rate of 5% per year.
Problem 39 :
Find the simple ineterest on $500 for 2 years at the rate of 7.5% per year.
Problem 40 :
Find the simple ineterest on $800 for 9 months at the rate of 5% per year.
Problem 41 :
In simple interest, a certain sum of money doubles itself in 15 years. In how many years will it triple itself?
Problem 42 :
Find the compound ineterest on $500 for 2 years at the rate of 10% per year, if interest is compounded annually.
Problem 43 :
Find the compound ineterest on $10000 for 1 year at the rate of 10% per year, if interest is compounded semi- annually.
Problem 44 :
In compound interest, a sum of money doubles itself in 20 years. In how many years will it become 4 times of itself?
1. Answer :
40 + 30 = ?
Both the two digit numbers have zero at one's place. So, add the digits at ten's place and take one zero along with the result.
4 + 3 = 7
Therefore,
40 + 30 = 70
2. Answer :
80 + 50 = ?
8 + 5 = 13
Therefore,
80 + 50 = 130
3. Answer :
= 46 + 30
= 40 + 6 + 30
= (40 + 30) + 6
= 70 + 6
= 76
4. Answer :
= 52 + 34
= 50 + 2 + 30 + 4
= (50 + 30) + (2 + 4)
= 80 + 6
= 86
5. Answer :
= 126 + 78
= 120 + 6 + 70 + 8
= (120 + 70) + (6 + 8)
= 190 + 14
= 190 + 10 + 4
= 200 + 4
= 204
6. Answer :
= 208 + 126
= 200 + 8 + 120 + 6
= (200 + 120) + (8 + 6)
= 320 + 14
= 334
7. Answer :
= 85 + 49
Here, 85 is close to the round figure 100. To make 85 as 100, we need to add 15 to 85. Take 15 from 49 and add it to 85 and do the rest of the process.
= 85 + 15 + 24
= 100 + 24
= 124
8. Answer :
= 291 + 25
= 291 + 9 + 16
= 300 + 16
= 316
9. Answer :
70 - 30 = ?
Both the two digit numbers have zero at one's place. So, Subtract the digits at ten's place and take one zero along with the result.
7 - 3 = 4
Therefore,
70 - 30 = 40
10. Answer :
80 - 50 = ?
8 - 5 = 3
Therefore,
80 - 50 = 30
11. Answer :
= 56 - 20
= 50 + 6 - 20
= (50 - 20) + 6
= 30 - 6
= 24
12. Answer :
= 84 - 55
= 84 - (50 + 5)
= 84 - 50 - 5
= 34 - 5
= 29
13. Answer :
= 126 - 78
= 126 - (70 + 8)
= 126 - 70 - 8
= 56 - 8
= 48
14. Answer :
= 208 - 126
= 208 - (100 + 26)
= 208 - 100 - 26
= 108 - 26
= 108 - (20 + 6)
= 108 - 20 - 6
= 88 - 6
= 82
15. Answer :
= 16 x 7
= (10 + 6) x 7
It is easier to multiply 10 by any number. Multiplying 10 by 7 results 70. Multiplying 6 by 7 results 42.
Add 70 and 42.
= 70 + 42
= 70 + 30 + 12
= 100 + 12
= 112
16. Answer :
= 12 x 25
4 times 25 is equal to 100. So, we can do the above multiplication as shown below.
= 3 x 4 x 25
= 3 x 100
= 300
17. Answer :
= 25 x 9
8 times 25 is equal to 200. To get the answer for 9 times 25, take 8 times 25 and add one 25 to the result.
= 200 + 25
= 225
18. Answer :
= 8 x 49
Consider the rounded figure near to 49, that is 50. So, we can write 50 as (50 - 1) and multiply it by 8 as shown below.
= 8 x (50 - 1)
To multiply 8 by 50, multiply 8 by 5 and take zero along with the result. 8 times 5 is 40. Then, 8 times 50 is 400.
= 400 - 8
= 392
19. Answer :
= 73 x 6
= (70 + 3) x 6
= 420 + 18
= 438
20. Answer :
= 9 x 999
= 9 x (1000 - 1)
= 9000 - 9
= 8991
21. Answer :
= 8 x 125
Consider the rounded figure near to 125, that is 100. So, we can write 125 as (100 + 25) and multiply it by 8 as shown below.
= 8 x (100 + 25)
= 800 + 200
= 1000
22. Answer :
= 103 x 9
= (100 + 3) x 9
= 900 + 27
= 927
23. Answer :
= 250 x 12
= 250 x (10 + 2)
= 2500 + 500
= 3000
24. Answer :
= 498 x 6
= 498 x 6
= (500 - 2) x 6
= 3000 - 12
= 2988
25. Answer :
12 x 18
Step 1 :
Choose one of the two numbers, larger one is preferred, that is 18. Add the digit in one's place in the other number to 18.
= 18 + 2
= 20
Step 2 :
Multiply 20 by 10. And also, multiply the digits in one's place of both the numbers.
20 x 10 = 200 |
2 x 8 = 16 |
Step 3 :
Add the results of the above two multiplications.
= 200 + 16
= 216
Therefore,
12 x 18 = 216
26. Answer :
16 x 17
Step 1 :
= 17 + 6
= 23
Step 2 :
23 x 10 = 230 |
6 x 7 = 42 |
Step 3 :
= 230 + 42
= 272
Therefore,
16 x 17 = 272
27. Answer :
18 x 19
Step 1 :
= 19 + 8
= 27
Step 2 :
27 x 10 = 270 |
9 x 8 = 72 |
Step 3 :
= 270 + 72
= 342
Therefore,
18 x 19 = 342
28. Answer :
12 x 13
Step 1 :
= 13 + 2
= 15
Step 2 :
15 x 10 = 150 |
2 x 3 = 6 |
Step 3 :
= 150 + 6
= 156
Therefore,
12 x 13 = 156
29. Answer :
19 x 16
Step 1 :
= 19 + 6
= 25
Step 2 :
25 x 10 = 250 |
9 x 6 = 54 |
Step 3 :
= 250 + 54
= 304
Therefore,
19 x 16 = 304
The method used in the answers (11 to 15) above will work only when there is 1 at the ten's place of both the two digit numbers (Times Table).
30. Answer :
10% of 54.32
To calculate 10% of 54.32, move the decimal point in 54.32, one digit to the left.
10% of 54.32 = 5.432
31. Answer :
10% of 820
In 820, there is no decimal point. So, we have to assume there is decimal point at the and.
= 10% of 820.
To calculate 10% of 820., move the decimal point in 820., one digit to the left
= 82.0
= 82
32. Answer :
= 20% of 500
= 2 x 10% of 500
= 2 x 50.0
= 2 x 50
= 100
33. Answer :
= 35% of 900
= 30% of 900 + 5% of 900
= 30% of 900 = 3 x 10% of 900 = 3 x 90 = 270 |
= 5% of 900 = ½ x 10% of 900 = ½ x 90 = 45 |
Add the above two results.
= 270 + 45
= 315
Therefore,
35% of 900 = 315
34. Answer :
= 5% of 370
= ½ x 10% of 370
= ½ x 37
= 18.5
35. Answer :
= 3% of 400
= 3 x 1% of 400.
To calculate 1% of 400., move the decimal point in 400. two digits to the left
= 3 x 4.00
= 3 x 4
= 12
36. Answer :
= 6% of 450
= 6 x 1% of 450.
To calculate 1% of 450., move the decimal point in 450. two digits to the left
= 6 x 4.50
= 6 x 4.5
We know that 2 times 4.5 is 9.
= 3 x 2 x 4.5
= 6 x 4.5
= 27
37. Answer :
= 7% of 90
= 7 x 1% of 90.
To calculate 1% of 90., move the decimal point in 90. two digits to the left
= 7 x 0.90
= 7 x 0.9
= 6.3
38. Answer :
Simple interest for one year :
= 5% of 700
= ½ x 10% x 700
= ½ x 70.0
= ½ x 70
= $35
Since we have to calculate simple interest for 3 years, multiply the above result by 3.
= 3 x $35
= $105
39. Answer :
Simple interest for one year :
= 7.5% of 500
= 7.5 x 1% x 500
= 7.5 x 5.00
= 7.5 x 5
= (7 + 0.5) x 5
= 35 + 2.5
= $37.50
Since we have to calculate simple interest for 2 years, multiply the above result by 2.
= 2 x $37.50
= $75
40. Answer :
Simple interest for one year :
= 5 % of 800
= ½ x 10% x 800
= ½ x 80
= $40
Simple interest for 3 months :
= $40 ÷ 4
= $10
Simple interest for 9 months :
= 3x $10
= $30
41. Answer :
If you invest $100, it will become $200 in 15 years.
So, interest earned in the first fifteen years :
= 200 - 100
= $100
In simple interest, interest earned for the same principal and same time period will always be same. Since $100 is the interest earned in the first fifteen years, the interest earned earned in the next fifteen years also (from year 16 to year 30) will be $100.
Principal = $100
Interest (year 1 to 15) = $100
Interest (year 16 to 30) = $100
Add the above amounts,
= 100 + 100 + 100
= $300
Therefore, the sum of money will triple itself in 30 years.
42. Answer :
Interest for the first year :
= 10% of 500
= 50.0
=$50
Principal for the second year :
= 500 + 50
= $550
Interest for the second year :
= 10% of 550
= 55.0
=$55
Total interest earned in 2 years :
= 50 + 55
= $105
43. Answer :
Interest for the first six months :
= ½ x (interest for one year)
= ½ x 10% of 10000
= ½ x 1000
= $500
Principal for the next six months :
= 10000 + 500
= $10500
Interest for the next six months :
= ½ x 10% of 10500
= ½ x 1050
= $525
Total interest earned in 2 years :
= 500 + 525
= $1025
44. Answer :
If you invest $100, it will become $200 in 20 years.
For the next twenty years years (from year 21 to year 40), the principal is $200 and it will double itself at the end of year 40. That is, it will become $400 at the end of 40 years.
Therefore, the sum of money will become 4 times of itself in 40 years.
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