Average
- 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.
- The average of 30 numbers is 12. The average of the first 20 of them is 11 and that of the next 9 is 10. The last number is
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Given , Sum of 30 numbers = 30 × 12 = 360
Sum of the first 20 numbers = 20 × 11 = 220
and Sum of the next 9 numbers = 9 × 10 = 90
∴ Last number = Sum of 30 numbers – Sum of the first 20 numbers – Sum of the next 9 numbersCorrect Option: D
Given , Sum of 30 numbers = 30 × 12 = 360
Sum of the first 20 numbers = 20 × 11 = 220
and Sum of the next 9 numbers = 9 × 10 = 90
∴ Last number = Sum of 30 numbers – Sum of the first 20 numbers – Sum of the next 9 numbers
Last number = 360 – 220 – 90
Last number = 360 – 310 = 50
- The average of 11 results is 50. If the average of the first six results is 49 and that of the last six is 52, the sixth no. is
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Here , Sum of 11 results = 50 × 11 = 550
Sum of the first six results = 49 × 6 = 294
and Sum of the last six results = 52 × 6 = 312
∴ Sixth result = Sum of the first six results + Sum of the last six results – Sum of 11 resultsCorrect Option: D
Here , Sum of 11 results = 50 × 11 = 550
Sum of the first six results = 49 × 6 = 294
and Sum of the last six results = 52 × 6 = 312
∴ Sixth result = Sum of the first six results + Sum of the last six results – Sum of 11 results
Sixth result = 294 + 312 – 550 = 56
- The average of eight successive numbers is 6.5. The average of the smallest and the greatest numbers among them will be :
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Here , eight successive numbers are -
y , y + 1 , y + 2 , y + 3 , y + 4 , y + 5 , y + 6 , y + 7
As we know that ,
Sum of given terms = Average × total number of terms
y + y + 1 + y + 2 + y + 3 + y + 4 + y + 5 + y + 6 + y + 7 = 6.5 × 8 = 52
⇒ 8y + 28 = 52
⇒ 8y = 52 – 28 = 24
⇒ y = 3Correct Option: B
Here , eight successive numbers are -
y , y + 1 , y + 2 , y + 3 , y + 4 , y + 5 , y + 6 , y + 7
As we know that ,
Sum of given terms = Average × total number of terms
y + y + 1 + y + 2 + y + 3 + y + 4 + y + 5 + y + 6 + y + 7 = 6.5 × 8 = 52
⇒ 8y + 28 = 52
⇒ 8y = 52 – 28 = 24
⇒ y = 3∴ Required average = 3 + 10 = 6.5 2
- 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
