Question

One of the two number is 5 times another number. If 21 is added to both the numbers, then one of the numbers become twice that of other new number. Find the numbers.​

Answer 1

Answer:

Linear Equations in One Variable

A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers? Thus, the required numbers are 7 and 35.

Thanks

Answer 2

Given :-

• One of the two numbers is 5 times the another number.

• 21 is added to both the numbers, then one of the numbers become twice that of other new numbers.

To Find :-

• What are the numbers.

Solution :-

Let,

$\leadsto \bf{First\: number =\: y}$

$\leadsto \bf{Second\: number =\: 5y}$

❒ 21 is added to both the numbers :

$\mapsto \sf First\: number =\: y + 21$

$\mapsto \sf Second\: number =\: 5y + 21$

According to the question,

$\implies \sf 5y + 21 =\: 2 \times (y + 21)$

$\implies \sf 5y + 21 =\: 2(y + 21)$

$\implies \sf 5y + 21 =\: 2y + 42$

$\implies \sf 5y - 2y =\: 42 - 21$

$\implies \sf 3y =\: 21$

$\implies \sf y =\: \dfrac{\cancel{21}}{\cancel{3}}$

$\implies \sf y =\: \dfrac{7}{1}$

$\implies \sf\bold{\purple{y =\: 7}}$

Hence, the required numbers are :

➲ First number :

$\longrightarrow \sf First\: number =\: y$

$\longrightarrow \sf\bold{\pink{First\: number =\: 7}}$

➲ Second number :

$\longrightarrow \sf Second\: number =\: 5y$

$\longrightarrow \sf Second\: number =\: 5 \times 7$

$\longrightarrow \sf\bold{\pink{Second\: number =\: 35}}$

$\begin{gathered}{\small{\bold{\underline{\therefore\: The\: numbers\: are\: 7\: and\: 35\: respectively\: .}}}}\\\end{gathered}$