Question

Two numbers are in ratio 2:3. If 5 is added to first and 5 is subtracted from second then the ratio become 3:2. find the numbers

Answer 1

Answer:

${\underline{\underline{\maltese{\textsf{\textbf{\:Given\::-}}}}}}$

• ➳ Two numbers are in ratio 2:3.
• ➳ After adding 5 in first and subtracting 5 in second number the ratio becomes 3:2.

$\begin{gathered}\end{gathered}$

${\underline{\underline{\maltese{\textsf{\textbf{\:To Find\::-}}}}}}$

• ➳ The numbers

$\begin{gathered}\end{gathered}$

${\underline{\underline{\maltese{\textsf{\textbf{\:Solution\::-}}}}}}$

★ Let the,

• ➳ First number be 2x.
• ➳ Second number be 3x.

$\rule{200}2$

★ According to the question

• ➳ Adding 5 in first number = (2x+5)
• ➳ Subtracting 5 in second number = (3x-5)

$\rule{200}2$

★ Now the equation will be

$\quad{: \implies{\sf{\dfrac{2x + 5}{3x - 5} = \dfrac{3}{2}}}}$

• By cross multiplication

$\quad{: \implies{\sf{(3x \times 3)-(5 \times 3)} = {(2x \times 2) +( 5 \times 2)}}}$

$\quad{: \implies{\sf{9x-15} = {4x+10}}}$

$\quad{: \implies{\sf{9x-4x} = {15+10}}}$

$\quad{: \implies{\sf{5x} = {25}}}$

$\quad{: \implies{\sf{x} = {\dfrac{25}{5}}}}$

$\quad{: \implies{\sf{x} = \cancel{\dfrac{25}{5}}}}$

$\quad{: \implies{\sf{x = 5}}}$

$\quad\dag{\underline{\boxed{\sf{x = 5}}}}$

$\rule{200}2$

★ Hence

• ➭ First number = 2×5 = 10
• ➭ Second number = 3×5 = 15

$\begin{gathered}\end{gathered}$

${\underline{\underline{\maltese{\textsf{\textbf{\:Verification\::-}}}}}}$

★ Checking our answer

$\quad{: \implies{\sf{\dfrac{2x + 5}{3x - 5} = \dfrac{3}{2}}}}$

• Substituting the values of x

$\quad{: \implies{\sf{\dfrac{(2 \times 5) + 5}{(3 \times 5) - 5} = \dfrac{3}{2}}}}$

$\quad{: \implies{\sf{\dfrac{10 + 5}{15 - 5} = \dfrac{3}{2}}}}$

$\quad{: \implies{\sf{\dfrac{15}{10} = \dfrac{3}{2}}}}$

$\quad{: \implies{\sf{\cancel{\dfrac{15}{10}} = \dfrac{3}{2}}}}$

$\quad{: \implies{\sf{\dfrac{3}{2} = \dfrac{3}{2}}}}$

$\quad\dag\underline{\boxed{\sf{LHS=RHS}}}$

• ➭ Hence Verified!

$\begin{gathered}\end{gathered}$

${\underline{\underline{\maltese{\textsf{\textbf{\:Answer\::-}}}}}}$

• ➳ The first number is 10.
• ➳ The second number is 15.

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Answer 2

Answer:

᱖Question :-

• Two numbers are in ratio 2:3. If 5 is added to first and 5 is subtracted from second then the ratio become 3:2. find the numbers

$\begin{gathered}\end{gathered}$

᱖Answer :-

• Let the numbers be 2x and 3x

According to the question,

$\leadsto$ (2x+5)/(3x-5)=3/2

• cross multiplication

$\leadsto$ 9x-15=4x+10

$\leadsto$ 9x-4x=15+10

$\leadsto$ 5x=25

$\leadsto$ x=25/5

$\leadsto$ x=5

$\begin{gathered}\end{gathered}$

Thus,

• $\dashrightarrow$ 2×5 = 10
• $\dashrightarrow$ 3×5 = 15

$\begin{gathered}\end{gathered}$

Hence, The numbers are 10 and 15.