The sum of two numbers is 4000. If 15% of one is equal to 25% of the other number, find the numbers.​

1 thought on “The sum of two numbers is 4000. If 15% of one is equal to 25% of the other number, find the numbers.​”

1. Given:

   • Sum of two numbers = 4000
   • 15% of one number is equal to 25% of another number.

   To Find:

   • What are numbers?

   Solution:

   As per given question, sum of numbers is equal to 4000.

   Let suppose that one number is x amd another is y.

   Therefore,

   • x + y = 4000 •••••••eq.(i)

   Now, given that 15% of one number is equal to 25% of another number.

   Therefore,

   • [tex]\small{\bf{\dfrac{15x}{100}~=~\dfrac{25y}{100}~~~~~•••••eq.(ii)}}[/tex]

   Solving equation (ii) :–

   [tex]\small{\bf{\dfrac{15x}{100}~=~\dfrac{25y}{100}}}[/tex]

   [Cancelling 100 because it is in both side]

   [tex]\implies\small{\bf{15x~=~25y}}[/tex]

   [tex]\implies\small{\bf{x~=~\dfrac{25y}{15}}}[/tex]

   • We found that value of x = 25y/15

   Putting value of ‘x’ in equation (i):–

   [tex]\small{\bf{x+y~=~4000}}[/tex]

   [tex]\implies\small{\bf{\dfrac{25y}{15}+y~=~4000}}[/tex]

   [tex]\implies\small{\bf{\dfrac{25y+15y}{15}~=~4000}}[/tex]

   [tex]\implies\small{\bf{\dfrac{40y}{15}~=~4000}}[/tex]

   [tex]\implies\small{\bf{40y~=~4000×15}}[/tex]

   [tex]\implies\small{\bf{y~=~\dfrac{4000×15}{40}}}[/tex]

   [tex]\implies\small{\bf{y~=~{\dfrac{\cancel{4000}×15}{\cancel{40}}}}}[/tex]

   [tex]\implies\small{\bf{y~=~100×15}}[/tex]

   [tex]\implies\small{\bf{\green{y~=~1500}}}[/tex]

   Now putting value of y in equation (ii)

   [tex]\small{\bf{x+y~=~4000}}[/tex]

   [tex]\implies\small{\bf{x+1500~=~4000}}[/tex]

   [tex]\implies\small{\bf{x~=~4000-1500}}[/tex]

   [tex]\implies\small{\green{\bf{x~=~2500}}}[/tex]

   Therefore,

   • [tex]\large{\underline{\boxed{\bf{\red{Two~numbers~are~1500~and~2500~}}}}}[/tex]

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