Average
- 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 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 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
- In a certain year, the average monthly income of a person was ₹ 3,400. For the first eight months of the year, his average monthly income was ₹ 3,160 and for the last five months, it was ₹ 4,120. His income in the eighth month of the year was
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Given that , average income of a person = ₹ 3,400
Sum of annual income of a person = ₹ ( 3,400 x 12 )
Sum of first eight month income of a person = ₹ ( 3160 x 8 )
Sum of last five month income of a person = ₹ ( 5 × 4120 )
∴ Person’s income in the eighth month = (3160 × 8 + 5 × 4120 – 12 × 3400)Correct Option: B
Given that , average income of a person = ₹ 3,400
Sum of annual income of a person = ₹ ( 3,400 x 12 )
Sum of first eight month income of a person = ₹ ( 3160 x 8 )
Sum of last five month income of a person = ₹ ( 5 × 4120 )
∴ Person’s income in the eighth month = (3160 × 8 + 5 × 4120 – 12 × 3400)
Person’s income in the eighth month = (25280 + 20600 – 40800) = 5080
- Out of seven given numbers, the average of the first four numbers is 4 and that of the last four numbers is also 4. If the average of all the seven numbers is 3, fourth number is
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Average of the first four numbers = 4
Sum of the first four numbers = 4 × 4
Average of the last four numbers = 4
Sum of the last four numbers = 4 × 4
Average of all the seven numbers = 3
Sum of the seven numbers = 3 × 7
∴ Fourth number = ( Sum of the first four numbers + Sum of the last four numbers ) - Sum of the seven numbersCorrect Option: D
Average of the first four numbers = 4
Sum of the first four numbers = 4 × 4
Average of the last four numbers = 4
Sum of the last four numbers = 4 × 4
Average of all the seven numbers = 3
Sum of the seven numbers = 3 × 7
∴ Fourth number = ( Sum of the first four numbers + Sum of the last four numbers ) - Sum of the seven numbers
Fourth number = (4 × 4 + 4 × 4 – 3 × 7)
Fourth number = (16 + 16 - 21) = 11
