Question

the sum of two numbers is 80.of the larger number exceeds four times the smaller one by 5,then the smaller number is:

Answer 1

$\bf{\underline{\underline \blue{Solution:-}}}$

$\sf\underline{\red{\:\:\: AnswEr:-\:\:\:}}$

• The larger number x = 65
• The smaller number y = 15

$\sf\underline{\red{\:\:\: Given:-\:\:\:}}$

• The sum of two numbers is 80.
• The larger number exceeds four times the smaller one by 5.

$\sf\underline{\red{\:\:\: Need\:To\: Find:-\:\:\:}}$

• The smaller number is = ?

$\bf{\underline{\underline \blue{Explanation:-}}}$

Let the larger number be x

And the smaller number be y.

$\sf\underline{\pink{\:\:\: A.T.Q:-\:\:\:}}$

The sum of two numbers is 80.

• $\textbf {x + y = 80}$..... (i)

If the larger number exceeds four times the smaller one by 5.

• $\textbf {x = 4y + 5}$
• $\textbf {x - 4y = 5}$ ..... (ii)

$\sf\underline{\green{\:\:\: Subtracting\:(ii) from \:(i), We \:Get :-\:\:\:}}$

$\dashrightarrow \sf {(x + y) - (x - 4y) = 80 - 5}$

$\dashrightarrow \sf {(x + y) - (x + 4y) = 75}$

$\dashrightarrow \sf {5y = 75}$

$\dashrightarrow \sf {y = \dfrac{\cancel{75}}{\cancel{5}}\:}$

$\dashrightarrow \sf {y = 15}$

$\sf\underline{\green{\:\:\: Now, \:putting \:y = 15\: in \:(i), \:We \:Have :-\:\:\:}}$

$\dashrightarrow \sf {x + y = 80}$

$\dashrightarrow \sf {x + 15 = 80}$

$\dashrightarrow \sf {x = 80 - 15}$

$\dashrightarrow \sf {x = 65}$

$\sf\underline{\orange{\:\:\: ThereFore:-\:\:\:}}$

• The larger number (x) = 65
• The smaller number (y) = 15

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Answer 2

Given :

Sum of two number is 80

Larger number exceeds four times the smaller one by 5

To Find :

Smaller Number

Solution :

Let larger number = x

and smaller number = y

Now

According to question :

Sum of two number is 80

So x + y = 80 ... (1)

and

Larger number exceeds four times the smaller one by 5

x = 4y + 5 ... (2)

Solving equation 1 and 2

x + y = 80

x = 80 - y

x = 4y + 5 ... (3)

putting value of x in equation 3

80 - y = 4y + 5

5y = 75

y = 15

x = 80 - 15 = 65

Thus, larger number is 65 and smaller number is 15.