Question

A positive number is 6 times another number. If 40 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

Answer 1

Answer:

Given :-

• A positive number is 6 times another number.
• 40 is added to both the numbers, then one of the new numbers becomes twice the other new number.

To Find :-

• What are the numbers.

Solution :-

Let,

$\mapsto \bf Another\: Number =\: a$

$\mapsto \bf Positive\: Number =\: 6a$

❒ 40 is added to both the numbers :

$\leadsto \sf Another\: Number =\: (a + 40)$

$\leadsto \sf Positive\: Number =\: (6a + 40)$

According to the question,

$\implies \sf 6a + 40 =\: 2(a + 40)$

$\implies \sf 6a + 40 =\: 2a + 80$

$\implies \sf 6a - 2a =\: 80 - 40$

$\implies \sf 4a =\: 40$

$\implies \sf a =\: \dfrac{\cancel{40}}{\cancel{4}}$

$\implies \sf a =\: \dfrac{10}{1}$

$\implies \sf\bold{\purple{a =\: 10}}$

Hence, the required numbers are :

❒ Another Number :

$\longrightarrow \sf Another\: Number =\: a$

$\longrightarrow \sf\bold{\red{Another\: Number =\: 10}}$

❒ Positive Number :

$\longrightarrow \sf Positive\: Number =\: 6a$

$\longrightarrow \sf Positive\: Number =\: 6 \times 10$

$\longrightarrow \sf\bold{\red{Positive\: Number =\: 60}}$

${\small{\bold{\underline{\therefore\: The\: numbers\: are\: 10\: and\: 60\: .}}}}$

Answer 2

Answer:

Given :-

A positive number is 6 times another number.

40 is added to both the numbers, then one of the new numbers becomes twice the other new number.

To Find :-

What are the numbers.

Solution :-

Let,

\mapsto \bf Another\: Number =\: a↦AnotherNumber=a

\mapsto \bf Positive\: Number =\: 6a↦PositiveNumber=6a

❒ 40 is added to both the numbers :

\leadsto \sf Another\: Number =\: (a + 40)⇝AnotherNumber=(a+40)

\leadsto \sf Positive\: Number =\: (6a + 40)⇝PositiveNumber=(6a+40)

According to the question,

\implies \sf 6a + 40 =\: 2(a + 40)⟹6a+40=2(a+40)

\implies \sf 6a + 40 =\: 2a + 80⟹6a+40=2a+80

\implies \sf 6a - 2a =\: 80 - 40⟹6a−2a=80−40

\implies \sf 4a =\: 40⟹4a=40

\implies \sf a =\: \dfrac{\cancel{40}}{\cancel{4}}⟹a=

4

40

\implies \sf a =\: \dfrac{10}{1}⟹a=

1

10

\implies \sf\bold{\purple{a =\: 10}}⟹a=10

Hence, the required numbers are :

❒ Another Number :

\longrightarrow \sf Another\: Number =\: a⟶AnotherNumber=a

\longrightarrow \sf\bold{\red{Another\: Number =\: 10}}⟶AnotherNumber=10

❒ Positive Number :

\longrightarrow \sf Positive\: Number =\: 6a⟶PositiveNumber=6a

\longrightarrow \sf Positive\: Number =\: 6 \times 10⟶PositiveNumber=6×10

\longrightarrow \sf\bold{\red{Positive\: Number =\: 60}}⟶PositiveNumber=60

{\small{\bold{\underline{\therefore\: The\: numbers\: are\: 10\: and\: 60\: .}}}}

∴Thenumbersare10and60.