Question : The average of n numbers is 42. If 75% of the numbers are increased by 4 each and the remaining numbers are decreased by 8 each, then what is the average of the numbers, so obtained?
Option 1: 44
Option 2: 42.5
Option 3: 43
Option 4: 43.8
Correct Answer: 43
Solution : The average of n numbers is 42, so the total sum of these numbers is 42n. If 75% of the numbers are increased by 4 each. The total increase in the sum of these numbers = 0.75n × 4 = 3n The remaining 25% of the numbers are decreased by 8 each. The total decrease in the sum of these numbers = 0.25n × 8 = 2n The new sum of the numbers = 42n + 3n – 2n = 43n Since the number of elements 'n' hasn't changed, the new average = $\frac{43n }{ n}$ = 43 Hence, the correct answer is 43.
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Question : The length of a rectangle is increased by 10% and breadth is decreased by 10%. The area of the new rectangle is:
Option 1: neither increased nor decreased.
Option 2: increased by 1%.
Option 3: decreased by 2%.
Option 4: decreased by 1%.
Question : The ratio between the two numbers is 3 : 4. If each number is increased by 6, the ratio becomes 4 : 5. What is the difference of the numbers?
Option 1: 1
Option 2: 3
Option 3: 6
Option 4: 8
Question : A number is first increased by 10% and then increased by 20%. The number, so obtained, is now decreased by 12%. What is the net increase or decrease percent in the original number?
Option 1: 16.16% increase
Option 2: 14.14% decrease
Option 3: 11.11% decrease
Option 4: 12.12% increase
Question : The ratio of two numbers is 3 : 5. If both numbers are increased by 8, the ratio becomes 13 : 19. What is the sum of the two numbers?
Option 1: 32
Option 2: 48
Option 3: 40
Option 4: 72
Question : The average of 19 numbers is 22.8. The average of the first ten numbers is 18.4 and that of the last ten numbers is 28.6. If the $10^{\text {th}}$ number is excluded from the given numbers, then what is the average of the remaining numbers? (Your answer should be nearest to an integer.)
Option 1: 21
Option 2: 23
Option 3: 22
Option 4: 20
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