Question

4.The difference between two positive numbers is 40 and the ratio of these integers is 1:3. Find the integers.​

Answer 1

★ Given :

Difference between 2 positive numbers= 40

ratio of integers = 1:3

★ To find:

the integers .

★ Solution :

1 : 3 , numbers are x and 3x

3x - x = 40

2x = 40

$x = \frac{\cancel{40}}{\cancel{2}} \\ \\ \\ x = 20$

first number = x = 20

second number = 3x = 3×20 = 60

$\purple{\therefore \: the\: integers \:are\: 20 \:and\: 60}$

★ Verification :

difference = 40

60 - 20 = 40

$ratio = \frac{1}{3} \\ \\ \\ \frac{\cancel{20}}{\cancel{60}} = \frac{1}{3} \\ \\ \\ \therefore \: ratio \: is \: equal\: to \: 1:3$

$\purple{Hence\: verified}$

Answer 2

Step-by-step explanation:

★ Given :

Difference between 2 positive numbers= 40

ratio of integers = 1:3

★ To find:

the integers .

★ Solution :

1 : 3 , numbers are x and 3x

3x - x = 40

2x = 40

\begin{gathered}x = \frac{\cancel{40}}{\cancel{2}} \\ \\ \\ x = 20\end{gathered}

x=

2

40

x=20

first number = x = 20

second number = 3x = 3×20 = 60

\purple{\therefore \: the\: integers \:are\: 20 \:and\: 60}∴theintegersare20and60

★ Verification :

difference = 40

60 - 20 = 40

\begin{gathered}ratio = \frac{1}{3} \\ \\ \\ \frac{\cancel{20}}{\cancel{60}} = \frac{1}{3} \\ \\ \\ \therefore \: ratio \: is \: equal\: to \: 1:3\end{gathered}

ratio=

3

1

60

20

=

3

1

∴ratioisequalto1:3