Question

The sum of four numbers is 126. The ratio of first number to the second number is 4: 3 respectively and the ratio of third number to the fourth number is 3: 4 respectively. Of the fourth number is greater than the second number by 30, find the average of first and third number

Answer 1

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GIVEN :

=> SUM OF FOUR NO. 126

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THE RATIO OF 1ST NO. TO 2ND NO. :

=> 4 : 3

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RATIO OF 3RD NO. TO 4TH NO. :

=> 3 : 4

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LET,

=> X AND Y BE THE COMMON MULTIPLE OF THESE RATIOS

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STEP 1ST :

FIND ALL THE NO.

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FIRST NO. :

=> 4 * X

=> 4X

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SECOND NO. :

=> 3 * X

=> 3X

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3RD NO. :

=> 3 * Y

=> 3Y

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4TH NO. :

=> 4 * Y

=> 4Y

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STEP 2 :

=> APPLY CONDITIONS AND FORM EQUATIONS

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FOURTH NO. IS GREATER THAN 2ND BY 30 :

=> 4Y = 30 + 3X

=> 4Y - 3X = 30

=> 3X-4Y=30 ....................... 1

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SUM OF ALL OF THEM IS 126

=> 1ST NO. + 2ND NO. + 3RD NO. + 4TH NO. = 126

=> 3X + 4X + 4Y + 3Y = 126

=> 7X + 7Y = 126

=> X + Y = 18 ....................... 2

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MULTIPLY THIS EQUATION BY 3 :

=> 3 ( X + Y = 18 )

=> 3X + 3Y = 54 .................... 3

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STEP 3 ;

FIND X AND Y

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SUBSTRACT THIS EQUATION FROM EQUATION 1

3X + 3Y = 54
-
3X - 4Y = -30
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=> 7Y = 84

=> Y = 84 / 7

$\huge\bold{y = 12}$

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PUT Y = 12 IN EQUATION 2

=> X + Y = 18

=> X + 12 = 18

=> X = 18 - 12

$\huge\bold{x = 6}$

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STEP 4 ;

FIND 1ST AND 3RD NO.

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1ST NO. :

=> 4X

=> 4 * 6

$\huge\bold{24}$

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3RD NO.

=> 3Y :

=> 3 * 12

$\huge\bold{36}$

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STEP 5 ;

FIND THE AVERAGE OF 1ST AND 3RD NO.

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AVERAGE :

=> SUM OF OBSERVATIONS / NO. OF OBSERVATIONS

=> 24 + 36 / 2

=> 60 / 2

$\huge\bold{30}$

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HOPE IT HELPED :

THANKS ........

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