Average
- The average of nine numbers is 50. The average of the first five numbers is 54 and that of the last three numbers is 52. Then the sixth number is
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Given , Sum of 9 numbers = 9 × 50 = 450
Sum of the first 5 numbers = 5 × 54 = 270
and Sum of the last 3 numbers = 3 × 52 = 156
∴ The sixth number = Sum of 9 numbers - Sum of the first 5 numbers - Sum of the last 3 numbersCorrect Option: C
Given , Sum of 9 numbers = 9 × 50 = 450
Sum of the first 5 numbers = 5 × 54 = 270
and Sum of the last 3 numbers = 3 × 52 = 156
∴ The sixth number = Sum of 9 numbers - Sum of the first 5 numbers - Sum of the last 3 numbers
The sixth number = 450 – 270 – 156 = 24
- Out of four numbers, the average of the first three is 15 and that of the last three is 16. If the last number is 19, the first is
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Given , Sum of first 3 numbers = 15 × 3 = 45
⇒ a + b + c = 45 ,
last number = d = 19
and Sum of the last three numbers = 16 × 3 = 48
⇒ b + c + d = 48
⇒ b + c = 48 – 19 = 29Correct Option: C
Given , Sum of first 3 numbers = 15 × 3 = 45
⇒ a + b + c = 45 ,
last number = d = 19
and Sum of the last three numbers = 16 × 3 = 48
⇒ b + c + d = 48
⇒ b + c = 48 – 19 = 29
∴ a + b + c = 45
⇒ a = 45 – 29 = 16
- The mean of 11 numbers is 35. If the mean of first 6 numbers is 32 and that of the last 6 numbers is 37, find the sixth number.
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Given , Sum of 11 numbers = 35 × 11 = 385
Sum of the first 6 numbers = 32 × 6 = 192
and Sum of the next 9 numbers = 37 × 6 = 222
∴ Sixth number = Sum of the first 6 numbers + Sum of the last 6 numbers – Sum of 11 numbersCorrect Option: B
Given , Sum of 11 numbers = 35 × 11 = 385
Sum of the first 6 numbers = 32 × 6 = 192
and Sum of the next 9 numbers = 37 × 6 = 222
∴ Sixth number = Sum of the first 6 numbers + Sum of the last 6 numbers – Sum of 11 numbers
Sixth number= 192 + 222 – 385 = 29
- Out of four numbers, the average of the first three is 18 and that of the last three is 16. If the last number is 19, the first is
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Here , Sum of first three = 18 × 3
⇒ a + b + c = 54
and Sum of last three = 16 × 3
⇒ b + c + d = 48
last number = 19
∴ a + b + c – b – c – d
⇒ 54 – 48 = 6Correct Option: D
Here , Sum of first three = 18 × 3
⇒ a + b + c = 54
and Sum of last three = 16 × 3
⇒ b + c + d = 48
last number = 19
∴ a + b + c – b – c – d
⇒ 54 – 48 = 6
⇒ a – d = 6
⇒ a – 19 = 6
⇒ a = 19 + 6 = 25
- The average of three numbers is 135. The largest number is 195 and the difference between the other two is 20. The smallest number is
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According to the question,
Sum of numbers = Average × Total number of terms
195 + y + ( y + 20 ) = 135 × 3
⇒ 2y + 215 = 405
⇒ 2y = 405 – 215 = 190Correct Option: B
According to the question,
Sum of numbers = Average × Total number of terms
195 + y + ( y + 20 ) = 135 × 3
⇒ 2y + 215 = 405
⇒ 2y = 405 – 215 = 190∴ y = 190 = 95 2
Required Smallest number is 95.
