Average
- Of three numbers, the first is 4 times the second and 3 times the third. If the average of all the three numbers is 95, what is the third number ?
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Let the third number be p,
∴ First number = 3p∴ Second number = 3p 4 According to the question, 3p + 3p + p = 3 × 95 4 ⇒ 12p + 3p + 4p = 285 4
⇒ 19p = 285 × 4⇒ 285 × 4 = 60 19
Aliter : Using Rule 15,Here, a = 4, b = 3 , X = 95 4
Correct Option: B
Let the third number be p,
∴ First number = 3p∴ Second number = 3p 4 According to the question, 3p + 3p + p = 3 × 95 4 ⇒ 12p + 3p + 4p = 285 4
⇒ 19p = 285 × 4⇒ 285 × 4 = 60 19
Aliter : Using Rule 15,Here, a = 4, b = 3 , X = 95 4 Third Number = 3 X 1 + b + ab Third Number = 3 × 95 1 + 3 + 4 × 3 4 4 Third Number = 3 × 4 × 95 = 60 4 + 3 + 12
- Of the three numbers, the first number is twice of the second and the second is thrice of the third number. If the average of these 3 numbers is 20, then the sum of the largest and smallest numbers is
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Let the third number be p.
∴ Second number = 3p
and first number = 6p
∴ 6p + 3p + p = 3 × 20
⇒ 10p = 60
⇒ p = 6
∴ Required sum = 6p + p = 7p = 7 × 6 = 42
Second method to solve this question with the help of given formulas :
Here, a = 2, b = 3, X = 20Largest Number = 3ab X 1 + b + ab Largest Number = 3 × 2 × 3 × 20 1 + 3 + 2 × 3
Correct Option: B
Let the third number be p.
∴ Second number = 3p
and first number = 6p
∴ 6p + 3p + p = 3 × 20
⇒ 10p = 60
⇒ p = 6
∴ Required sum = 6p + p = 7p = 7 × 6 = 42
Second method to solve this question with the help of given formulas :
Here, a = 2, b = 3, X = 20Largest Number = 3ab X 1 + b + ab Largest Number = 3 × 2 × 3 × 20 1 + 3 + 2 × 3 Largest Number = 18 × 20 = 36 10 Smallest Number = 3 X 1 + b + ab Smallest Number = 3 × 20 1 + 3 + 2 × 3 Smallest Number = 3 × 20 = 6 10
Sum = 36 + 6 = 42
- Among three numbers, the first is twice the second and thrice the third. If the average of the three numbers is 49.5, then the difference between the first and the third number is
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Let the second number be p.
∴ First number = 2p∴ Third number = 2p 3 ∴ 2p + p + 2p = 49.5 × 3 3
⇒ 6p + 3p + 2p = 49.5 × 9 = 445.5
⇒ 11p = 445.5⇒ p = 445.4 = 40.5 11 ∴ Required difference = 2p - 2p = 4p 3 3 Required difference = 4 × 40.5 = 54 3
Aliter : Using Rule 15,Here, a = 2, b = 3 , X = 49.5 2 First Number = 3ab X 1 + b + ab First Number = 3 × 2 × 3 × 49.5 2 1 + 3 + 2 × 3 2 2
Correct Option: A
Let the second number be p.
∴ First number = 2p∴ Third number = 2p 3 ∴ 2p + p + 2p = 49.5 × 3 3
⇒ 6p + 3p + 2p = 49.5 × 9 = 445.5
⇒ 11p = 445.5⇒ p = 445.4 = 40.5 11 ∴ Required difference = 2p - 2p = 4p 3 3 Required difference = 4 × 40.5 = 54 3
Aliter : Using Rule 15,Here, a = 2, b = 3 , X = 49.5 2 First Number = 3ab X 1 + b + ab First Number = 3 × 2 × 3 × 49.5 2 1 + 3 + 2 × 3 2 2 First Number = 18 × 49.5 2 11 2 First Number = 18 × 49.5 = 18 × 4.5 11 First Number = 18 × 45 = 81 10 Third Number = 3 X 1 + b + ab Third Number = 3 × 49.5 1 + 3 + 2 × 3 2 2 Third Number = 3 × 49.5 11 2
Third Number = 6 × 4.5 = 27
Difference = 81 – 27 = 54
- The average of three numbers is 40. The first number is twice the second and the second one is thrice the third number. The difference between the largest and the smallest numbers is
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Let the third number be p.
∴ Second number = 3p
First number = 6p∴ 6p + 3p + p = 40 3
⇒ 10p = 120 ⇒ p = 12
∴ Required difference = 6p – p = 5p = 5 × 12 = 60
Second method to solve this question with the help of given formulas :
Here, a = 2, b = 3, X = 40Largest Number = First Number = 3ab × X 1 + b + ab Largest Number = 3 × 2 × 2 × 40 1 + 3 + 2 × 2
Correct Option: D
Let the third number be p.
∴ Second number = 3p
First number = 6p∴ 6p + 3p + p = 40 3
⇒ 10p = 120 ⇒ p = 12
∴ Required difference = 6p – p = 5p = 5 × 12 = 60
Second method to solve this question with the help of given formulas :
Here, a = 2, b = 3, X = 40Largest Number = First Number = 3ab × X 1 + b + ab Largest Number = 3 × 2 × 2 × 40 1 + 3 + 2 × 2 Largest Number = 18 × 40 = 72 10 Smallest Number = Third Number = 3 × X 1 + b + ab Smallest Number = 3 × 40 1 + 3 + 2 × 3 Smallest Number = 3 × 40 = 12 10
Difference = 72 – 12 = 60
- The average of three numbers is 28, the first number is half of the second, the third number is twice the second, then the third number is
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Let the second number be p.
Then first number = p 2
and third number = 2pAccording to the question, p + p + 2p = 28 × 3 2 ⇒ p + 2p + 4p = 28 × 3 2
⇒ 7p = 28 × 3 × 2⇒ 168 = 24 7
∴ Third number = 2 × 24 = 48
Second method to solve this question with the help of given formulas :
Here, a = 1 , b = 1 , X = 28 2 2 Third number = 3 × X 1 + b + ab
Correct Option: A
Let the second number be p.
Then first number = p 2
and third number = 2pAccording to the question, p + p + 2p = 28 × 3 2 ⇒ p + 2p + 4p = 28 × 3 2
⇒ 7p = 28 × 3 × 2⇒ 168 = 24 7
∴ Third number = 2 × 24 = 48
Second method to solve this question with the help of given formulas :
Here, a = 1 , b = 1 , X = 28 2 2 Third number = 3 × X 1 + b + ab Third number = 3 × 28 1 + 1 + 1 × 1 2 2 2 Third number = 3 × 28 4 + 2 + 1 4 Third number = 3 × 4 × 28 = 48 7
