Question

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

Answer 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,

• $\small{\bf{\dfrac{15x}{100}~=~\dfrac{25y}{100}~~~~~•••••eq.(ii)}}$

Solving equation (ii) :-

$\small{\bf{\dfrac{15x}{100}~=~\dfrac{25y}{100}}}$

[Cancelling 100 because it is in both side]

$\implies\small{\bf{15x~=~25y}}$

$\implies\small{\bf{x~=~\dfrac{25y}{15}}}$

• We found that value of x = 25y/15

Putting value of 'x' in equation (i):-

$\small{\bf{x+y~=~4000}}$

$\implies\small{\bf{\dfrac{25y}{15}+y~=~4000}}$

$\implies\small{\bf{\dfrac{25y+15y}{15}~=~4000}}$

$\implies\small{\bf{\dfrac{40y}{15}~=~4000}}$

$\implies\small{\bf{40y~=~4000×15}}$

$\implies\small{\bf{y~=~\dfrac{4000×15}{40}}}$

$\implies\small{\bf{y~=~{\dfrac{\cancel{4000}×15}{\cancel{40}}}}}$

$\implies\small{\bf{y~=~100×15}}$

$\implies\small{\bf{\green{y~=~1500}}}$

Now putting value of y in equation (ii)

$\small{\bf{x+y~=~4000}}$

$\implies\small{\bf{x+1500~=~4000}}$

$\implies\small{\bf{x~=~4000-1500}}$

$\implies\small{\green{\bf{x~=~2500}}}$

Therefore,

• $\large{\underline{\boxed{\bf{\red{Two~numbers~are~1500~and~2500~}}}}}$