Question

The difference of two numbers is 4,496. If 2.5% ofone number is 22.5% of the other number, thenfind the two numbers.​

Answer 1

$\purple{\bf{\underline{Given:-}}}$

▪The difference of two numbers is 4,496.

▪2.5% of one number is 22.5% of the other number.

$\pink{\bf{\underline{To\:Find:-}}}$

▪The two numbers.

$\huge\red{\bf{\underline{Solution:-}}}$

Let the two numbers be 'x' and 'y'.

According to the 1ˢᵗ condition,

$\bold{x - y = 4496}......(i)$

$⟹ \bold{ - y= 4496 - x}$

$⟹ \bold{y = x - 4496}$

According to the 2ⁿᵈ condition,

2.5% of x = 22.5% of y

$⟹ \bold{ \frac{2.5}{100} \times x = \frac{22.5}{100} \times y }......(ii)$

$⟹ \bold{\frac{2.5x}{100} = \frac{22.5y}{100} }$

$⟹ \bold{2.5x = 22.5y}$

$⟹ \bold{2.5x = 22.5(x - 4496)}$

$⟹ \bold{2.5x =22.5x - 101160}$

$⟹ \bold{2.5x - 22.5x = - 101160}$

$⟹ \bold{ - 20 x= - 101160}$

$⟹ \bold{x = \frac{ - 101160}{ - 20} }$

$\bold{∴x = 5058}$

Now, from the equation (1)

$\bold{x - y = 4496}$

$⟹ \bold{5058 - y = 5596}$

$⟹ \bold{ - y = 4496 - 5058}$

$⟹ \bold{- y = - 562}$

$\bold{∴y = 562}$

$\bold\blue{\bf{So,\:the\:two\:numbers\:are:\:5058\:and\:562.}}$

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$\pink {\sf {Hope\:It\:Helps\:Uh!!!}}$