Question

Two numbers are in the ratio 5 : 7. If the sum of these numbers is 84, find the numbers.

Answer 1

Let x is included in the ratio.Then,

First number = 5 x .

Second number = 7 x.


According to question,

Sum of these two numbers = 84

5 x + 7 x = 84

12 x = 84 

x = 84 / 12

x = 7.

First number  = 5 x = 5 * 7 = 35.

Second number = 7 x = 7 * 7 = 49.


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Verification; 

First number : Second number = 5 : 7

35 : 49 = 5 : 7

5 : 7 = 5 : 7

First condition verified.Now second one,

Sum of these two numbers = 84

35 + 49 = 84

84 = 84.

Second condition also verified.So, numbers are 35 and 49.

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Answer 2

Let the no be x, y
X/y = 5/7
5y = 7x
X+y = 84
Multiply by 5
5x+5y =84*5
5x+7x = 420
12x =420
X=420/12

Put these value in 1st eqn and get Y