Average
- In a class, the average score of girls in an examination is 73 and that of boys is 71. The average score for the whole class is 71.8. Find the percentage of girls.
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Let the number of boys be p and that of girls be q.
∴ 71p + 73q = 71.8 (p + q)
⇒ 71.8p – 71p = 73q – 71.8q
⇒ 0.8p = 1.2q⇒ p = 1.2 = 12 = 3 q 0.8 8 2 ⇒ p + 1 = 3 + 1 ⇒ p + q = 5 q 2 q 2
Correct Option: A
Let the number of boys be p and that of girls be q.
∴ 71p + 73q = 71.8 (p + q)
⇒ 71.8p – 71p = 73q – 71.8q
⇒ 0.8p = 1.2q⇒ p = 1.2 = 12 = 3 q 0.8 8 2 ⇒ p + 1 = 3 + 1 ⇒ p + q = 5 q 2 q 2 ∴ Percentage of girls = q × 100 = 2 × 100 = 40% p + q 5
- The average weight of 40 children of a class is 36.2 kg. When three more children with weight 42.3 kg, 39.7 kg and 39.5 kg join the class, the average weight of the 43 children in the class is
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According to question ,
Total weight of 40 children = 40 × 36.2 kg = 1448 kg
Total weight of 43 children = 1448 + 42.3 + 39.7 + 39.5 = 1569.5 kgCorrect Option: B
According to question ,
Total weight of 40 children = 40 × 36.2 kg = 1448 kg
Total weight of 43 children = 1448 + 42.3 + 39.7 + 39.5 = 1569.5 kg
∴ Required average weight = 15695 ÷ 43 = 36.5 kg
- If the mean of 4 observations is 20, when a constant ‘C’ is added to each observation, the mean becomes 22. The value of C is :
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Given ,The mean of 4 observations = 20
Total of 4 observations = 20 × 4
When a constant ‘C’ is added to each observation, then
New mean = 22
Total of new observations = 22 × 4Correct Option: C
Given ,The mean of 4 observations = 20
Total of 4 observations = 20 × 4
When a constant ‘C’ is added to each observation, then
New mean = 22
Total of new observations = 22 × 4
⇒ 4C = 22 × 4 – 20 × 4 = 88 – 80 = 8
⇒ C = 8 ÷ 4 = 2
- The average of six numbers is 32. If each of the first three numbers is increased by 2 and each of the remaining three numbers is decreased by 4, then the new average is
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Here , The average of six numbers = 32
If each of the first three numbers is increased by 2 and each of the remaining three numbers is decreased by 4 , then
Change = 2 × 3 – 3 × 4 = – 6Correct Option: C
Here , The average of six numbers = 32
If each of the first three numbers is increased by 2 and each of the remaining three numbers is decreased by 4 , then
Change = 2 × 3 – 3 × 4 = – 6∴ New average = 32 - 6 = 31 6
- The average of five numbers is 7. When three new numbers are included, the average of the eight numbers becomes 8.5. The average of the three new numbers is
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Given that , The average of five numbers = 7
Sum of five numbers = 5 × 7
When three new numbers are included, then
The average of 8 numbers = 8.5
Sum of 8 numbers = 8 × 8.5
Sum of the three new numbers = 8 × 8.5 – 5 × 7 = 68 – 35Correct Option: C
Given that , The average of five numbers = 7
Sum of five numbers = 5 × 7
When three new numbers are included, then
The average of 8 numbers = 8.5
Sum of 8 numbers = 8 × 8.5
Sum of the three new numbers = 8 × 8.5 – 5 × 7 = 68 – 35
Sum of the three new numbers = 33
∴ Required average = 33 ÷ 3 = 11
