Average
- Of the three numbers, second is twice the first and also thrice the third. If the average of the three numbers is 44, the largest number is :
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Let third number be p.
∴ Second number = 3pand first number = 3 p 2 Now, p + 3p + 3p = 3 × 44 2 ⇒ 8p + 3p = 3 × 44 2
⇒ 11p = 6 × 44
Correct Option: B
Let third number be p.
∴ Second number = 3pand first number = 3 p 2 Now, p + 3p + 3p = 3 × 44 2 ⇒ 8p + 3p = 3 × 44 2
⇒ 11p = 6 × 44⇒ p = 6 × 44 = 24 11
The largest number = 3p = 3 × 24 = 72
- Of the three numbers, first is twice the second and second is twice the third. The average of three numbers is 21. The smallest of the three numbers is
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Let the third number be n.
∴ The second number = 2n
and the third number = 2 × 2n = 4nAccording to the question, 4n + 2n + n = 21 3
⇒ 7n = 21 × 3⇒ n = 21 × 3 = 9 7
Second method to solve this question :
a = 2, b = 2, y = 21First number = 3ab y 1 + b + ab First number = 3 × 2 × 2 × 21 1 + 2 + 4
Correct Option: A
Let the third number be n.
∴ The second number = 2n
and the third number = 2 × 2n = 4nAccording to the question, 4n + 2n + n = 21 3
⇒ 7n = 21 × 3⇒ n = 21 × 3 = 9 7
Second method to solve this question :
a = 2, b = 2, y = 21First number = 3ab y 1 + b + ab First number = 3 × 2 × 2 × 21 1 + 2 + 4 First number = 12 × 21 = 36 7 Second number = 3b y 1 + a + ab Second number = 3 × 2 × 21 = 18 7 Third number = 3 y 1 + a + ab Third number = 3 × 21 = 9 7
- The average monthly salary of 19 members of a group is Rs. 16000. If one more member whose monthly salary is Rs. 20000 joins the group, then the average salary of the group is
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The average monthly salary of 19 members of a group = Rs. 16000.
A member whose monthly salary = Rs. 20000Required average = Rs. 
16000 × 19 + 20000 
20 Required average = Rs. 304000 + 20000 20 Required average = Rs. 324000 20
Required average = Rs. 16200
Second method to solve this question ,
Difference = Rs. (20000 – 16000) = Rs. 4000
Correct Option: B
The average monthly salary of 19 members of a group = Rs. 16000.
A member whose monthly salary = Rs. 20000Required average = Rs. 16000 × 19 + 20000 20 Required average = Rs. 304000 + 20000 20 Required average = Rs. 324000 20
Required average = Rs. 16200
Second method to solve this question ,
Difference = Rs. (20000 – 16000) = Rs. 4000∴ Increase in average = 4000 20
Increase in average = Rs. 200
∴ Required average = Rs. (16000 + 200) = Rs. 16200
- Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, then difference of first and third number is
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Let the numbers be 2k, k and 4k respectively
∴ Average = 2k + k + 4k 3 ⇒ 7k = 56 3 ⇒ k = 3 × 56 = 24 7
∴ First number = 2k = 2 × 24 = 48
Third number = 4k = 4 × 24 = 96
∴ Required difference = Third number - First number = 96 – 48 = 48
Second method to solve this question with the help of given formulas :
Here, a = 2, b = 1/4 , X = 56First number = 3ab × X 1 + b + ab First number = 3 × 2 × 1 × 56 4 1 + 1 + 2 × 1 4 4
Correct Option: D
Let the numbers be 2k, k and 4k respectively
∴ Average = 2k + k + 4k 3 ⇒ 7k = 56 3 ⇒ k = 3 × 56 = 24 7
∴ First number = 2k = 2 × 24 = 48
Third number = 4k = 4 × 24 = 96
∴ Required difference = Third number - First number = 96 – 48 = 48
Second method to solve this question with the help of given formulas :
Here, a = 2, b = 1/4 , X = 56First number = 3ab × X 1 + b + ab First number = 3 × 2 × 1 × 56 4 1 + 1 + 2 × 1 4 4 First number = 3 × 4 × 56 = 48 2 4 + 1 + 2 Third number = 3 × X 1 + b + ab Third number = 3 × 56 1 + 1 + 2 × 1 4 4 Third number = 3 × 4 × 56 = 96 4 + 4 + 2
Required difference = 96–48 = 48
- 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
