The difference between two numbers is 1600. I | vedclass

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Question

(A) Let the two numbers be $x$ and $y$,where $x > y$.According to the problem,the difference between the numbers is $x - y = 1600$.Also,$7.5\%$ of $x

Vedclass · Accepted Answer

$2400, 4000$

Vedclass · Answer

(A) Let the two numbers be $x$ and $y$,where $x > y$.According to the problem,the difference between the numbers is $x - y = 1600$.Also,$7.5\%$ of $x = 12.5\%$ of $y$.This can be written as $\frac{7.5}{100} x = \frac{12.5}{100} y$.Multiplying both sides by $100$,we get $7.5x = 12.5y$.Dividing both sides by $2.5$,we get $3x = 5y$,which implies $x = \frac{5}{3}y$.Substitute $x = \frac{5}{3}y$ into the first equation: $\frac{5}{3}y - y = 1600$.$\frac{2y}{3} = 1600$.$2y = 4800$,so $y = 2400$.Now,$x = 1600 + 2400 = 4000$.Thus,the two numbers are $4000$ and $2400$.

The difference between two numbers is $1600$. If $7.5\%$ of one number is equal to $12.5\%$ of the other number,find the two numbers.

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