two numbers are in the ratio of 1:2 if 7 is added to both and new ratio is 3:5 find the greatest number​

2 thoughts on “two numbers are in the ratio of 1:2 if 7 is added to both and new ratio is 3:5 find the greatest number​”

1. Answer:

   The greatest number is 28.

   Explanation:

   Given ratio of two numbers is – 1 : 2

   If 7 is added to both the numbers the ratio becomes 3 : 5

   Let’s assume,

   • smallest number = 1x
   • And, greater number = 2x

   Adding 7 to both the numbers we get,

   • Smallest number = (1x + 7)
   • Greater number = (2x + 7)

   Now,

   Forming in ratio :

   ⇒ (1x + 7) : (2x + 7)

   But, it’s given the ratio becomes 3 : 5

   According to the question,

   ⇒ (1x + 7)/(2x + 7) = 3/5

   ⇒ 5(1x + 7) = 3(2x + 7) [Cross multiplication ]

   ⇒ 5x + 35 = 6x + 21

   ⇒ 35 – 21 = 6x – 5x

   ⇒ 14 = x

   ∴ The value of ‘x’ is 14.

   Hence, the greatest number is,

   ⇒ 2x = 2(14) = 28

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2. Answer:–

   According to the Question

   Let the ratio be x : 2x

   It is given that 7 is added to the given number so new ratio is 3:5 .

   [tex]:\implies[/tex] x +7 = 2x+7

   Now, we can also write this ratio in fraction .

   [tex]:\implies[/tex] x+7/2x+7

   After adding 7 both side new ratio is 3:5 . So we can aslo write in fraction.

   [tex]:\implies[/tex] 3/5

   Equate the equation (according to the question)

   [tex]:\implies[/tex] x+7/2x+7 = 3/5

   [tex]:\implies[/tex] 5(x+7) = 3(2x+7)

   [tex]:\implies[/tex] 5x +35 = 6x + 21

   [tex]:\implies[/tex] 35 –21 = 6x -5x

   [tex]:\implies[/tex] 14 = x

   [tex]:\implies[/tex] x = 14

   So, the value of x is 14

   Greatest number = 2x = 2×14 = 28

   • Hence, the greatest number is 28 .

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