##### Two numbers are in the ratio 1:2 . If 7 is added to both , their ratio changes to 3:5 . Find the greatest number ?

_{By Akshaya, Posted on 06/04/2021 - 4 Comments}

##### Answers (4)

_{ Posted by Harshdev Jhirmiria on 08/04/2021 }

Let the two numbers be x and y.

Therefore, x/y=1:2

2x=1y

y=2x.........(i)

When 7 is added to both, x+7/y+7=3/5

X+7/y+7=3/5

5x+35=3y+21

5x-3y=-14.......(ii)

Now, by substituting in equation (ii)

5x -3y=-14

5x-3(2x)=-14

5x-6x=-14

**X=14**

Now by substituting X value in equation (i)

Y=2x

Y=2×14

__Y=28__

__Therefore the greater number is 28__.

_{ Posted by Hussaina on 08/04/2021 }

let 1 : 2 be x : 2x

according to the question, x+7/2x+7 = 3/5

cross-multiplication, 5(x+7) = 3(2x+7)

5x+35 = 6x+21

35-21 = 6x-5x

14 = x

as x=14, 2x=28.

therefore when 7 is added to the numerator and denominator, the ration becomes 21 : 35

Hence, the answer is i.e., the greatest number is 35.

_{ Posted by Prasad Mahadeo Sonone on 07/04/2021 }

Let 2 numbers be x and y

From condition 1,

x/y = 1/2 that implies 2x=y ......(1)

From condition 2,

(x+7)/(y+7) = 3/5

That implies

3y+21 = 5x+35

(5x+14)/3=y .....(2)

Subtracting (2)-(1)

(5x+14)/3 - 2x = 0

Hence

(5x +14 -6x)/3 = 0

(-x +14) = 0

-x = -14

x = 14

Substituting value of 'x' in equation (1)

2×14 = y

y = 28

The greatest number is 28

_{ Posted by Archana Sood on 07/04/2021 }

Suppose the numbers are x and 2x. The ratio is 1:2. So x/2x = 1/2

if 7 is added, their ratio changes to 3:5.

x+7/2x+7 = 3/5.

5(x+7) = 3(2x+7)

6x+21 = 5x+35

x = 14

so the numbers are 14 and 28 and 28 is the greatest number

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