Average
- Six friends have an average height of 167 cms. A boy with height 162 cm leaves the group. Find the new average height.
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Total height of 5 friends = (6 × 167 – 162) cm.
Total height of 5 friends = (1002 – 162) cm.
Total height of 5 friends = 840 cm.Correct Option: A
Total height of 5 friends = (6 × 167 – 162) cm.
Total height of 5 friends = (1002 – 162) cm.
Total height of 5 friends = 840 cm.∴ Required average = 840 = 168 cm. 5
- The average of 1, 3, 5, 7, 9, 11, -------- to 25 terms is
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Sum of first n odd natural numbers = n²
∴ Their average = n² = n n
Correct Option: B
Sum of first n odd natural numbers = n²
∴ Their average = n² = n n
∴ Required average = 25 , because n = 25
- A librarian purchased 50 story– books for his library. But he saw that he could get14 more books by spending Rs. 76 more and the average price per book would be reduced by Re. 1. The average price (in Rs.) of each book he bought, was :
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Let the average cost of each book bought (of 64 books) be ₹ y.
According to the question,
64 × y – 50(y + 1) = 76
⇒ 64y – 50y – 50 = 76
⇒ 14y = 76 + 50 = 126Correct Option: B
Let the average cost of each book bought (of 64 books) be ₹ y.
According to the question,
64 × y – 50(y + 1) = 76
⇒ 64y – 50y – 50 = 76
⇒ 14y = 76 + 50 = 126⇒ y = 126 = 9 14
∴ Required average price = 9 + 1 = ₹ 10
- The average weight of 3 men A, B and C is 84 kg. Another man D joins the group and the average now becomes 80 kg. If another man E whose weight is 3 kg more then that of D, replaces A, then the average weight of B, C, D and E becomes 79 kg. Then weight of A is
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D’s weight = 80 × 4 – 84 × 3
D’s weight = 320 – 252 = 68 kg.
E’s weight = 68 + 3 = 71 kg.
Total weight of (A + B + C + D + E) = 84 × 3 + 68 + 71
Total weight of (A + B + C + D + E) = 252 + 68 + 71 = 391 kg.
Total weight of (B + C + D + E) = 79 × 4 = 316 kg.Correct Option: C
D’s weight = 80 × 4 – 84 × 3
D’s weight = 320 – 252 = 68 kg.
E’s weight = 68 + 3 = 71 kg.
Total weight of (A + B + C + D + E) = 84 × 3 + 68 + 71
Total weight of (A + B + C + D + E) = 252 + 68 + 71 = 391 kg.
Total weight of (B + C + D + E) = 79 × 4 = 316 kg.
∴ A’s weight = Total weight of (A + B + C + D + E) - Total weight of (B + C + D + E)
A’s weight = 391 – 316 = 75 kg.
- The average of some natural numbers is 15. If 30 is added to first number and 5 is subtracted from the last number the average becomes 17.5 then the number of natural number is
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Number of natural numbers = p
∴ Their sum = 15p
According to the question,
15p + 30 – 5 = p × 17.5
⇒ 17.5p – 15p = 25
⇒ 2.5p = 25Correct Option: D
Number of natural numbers = p
∴ Their sum = 15p
According to the question,
15p + 30 – 5 = p × 17.5
⇒ 17.5p – 15p = 25
⇒ 2.5p = 25
⇒ p = 25/2.5 = 10
