The sum of three positive numbers is 18 and their product is 162

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11.

There is a number consisting of two digits, the digit in the units' place is twice that in the tens' place and if 2 be subtracted from the sum of the digits, the difference is equal to 1 over 6th of the number. The number is

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12.

The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, then the sum of squares of the numbers is

  • 120

  • 126

  • 132

  • 132


B.

126

Let the three numbers be x, y and z.
According to the question, we have three equations
x + y + z = 18               ...(i)
xyz = 162                      ...(ii)
and x + y = z                 ...(iii)
From equation (i),
   z + z = 18 
 ⟹   2z =  18 ⟹  z = 9
∴     xyz = 162
⟹   xy = 162/9 = 18    ...(iv)
therefore space space space left parenthesis straight x minus straight y right parenthesis squared space equals space left parenthesis straight x plus straight y right parenthesis squared space minus space 4 xy
space space space space space equals space left parenthesis 9 right parenthesis squared space minus space 4 space cross times space 18
space space space space space space equals space 81 space minus space 72 space equals space space 9
therefore space space space space straight x minus straight y space equals space 3
therefore space space space space straight x space plus space straight y space plus space straight x space minus straight y space equals space 9 space plus space 3
rightwards double arrow space space space space space space 2 straight x space equals space 12 space space rightwards double arrow space space space straight x space space equals space 6

therefore space space space space space straight x space plus space straight y space plus space straight z space equals space 18
rightwards double arrow space space space 6 space plus space straight y space plus space 9 space equals space 18
rightwards double arrow space space space space straight y space equals space 18 space minus space 15 space equals space 3
therefore space space space straight x squared plus straight y squared plus straight z squared
space space space space equals space left parenthesis 6 right parenthesis squared space plus space left parenthesis 3 right parenthesis squared space plus space left parenthesis 9 right parenthesis squared
space space space space equals 36 space plus space 9 space plus space 81 space equals space 126 space




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13.

The greater of the two numbers whose product is 900 and the sum exceeds their difference by 30 is

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14.

Sum of three consecutive integers is 51. The middle one is

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15.

The reciprocals of the squares of the numbers 1 1 half space and space 1 1 third are in the ratio:

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16.

Sum of two numbers is thrice their difference. Their ratio is 

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17.

If 4 over 5 th of a number exceeds its 3 over 4 th by 8, then the number is:

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18.

Among three numbers, second is twice the first and also thrice the third. If the average of the three numbers is 33, then the largest number is

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19.

If the sum of two numbers be multiplied by each number separately, the products so obtained are 247 and 114. The sum of the numbers is

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20.

If 21 is added to a number, it becomes 7 less than thrice of the number, Then, the number is

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