The ages of Ram and Shyam are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.
Answers
Answer:
Ram is 20 years old and Shyam is 28 years old.
Step-by-step explanation:
Given :
Ratio of present ages = 5 : 7
Ratio of ages after 4 years = 3 : 4
To find :
Their present ages
Solution :
Let the present ages be -
Ram as 5x
Shyam as 7x
\begin{gathered}\sf{\longrightarrow} \: \frac{5x + 4}{7x + 4} = \frac{3}{4} \\ \\ \sf{\longrightarrow} \: 4(5x + 4) = 3(7x + 4) \\ \\ \sf{\longrightarrow} \: 20x + 16 = 21x + 12 \\ \\ \sf{\longrightarrow} \: 21x - 20x = 16 - 12 \\ \\ \sf{\longrightarrow} \: x = 4\end{gathered}
⟶
7x+4
5x+4
=
4
3
⟶4(5x+4)=3(7x+4)
⟶20x+16=21x+12
⟶21x−20x=16−12
⟶x=4
\rule{300}{1.5}
★ Value of 5x
\begin{gathered}\sf{\longrightarrow} \: 5(4) \\ \\ \sf{\longrightarrow} \: 20\end{gathered}
⟶5(4)
⟶20
Ram's present age = 20 years old
\rule{300}{1.5}
★ Value of 7x
\begin{gathered}\sf{\longrightarrow} \: 7(4) \\ \\ \sf{\longrightarrow} \: 28\end{gathered}
⟶7(4)
⟶28
Shyam's present age = 28 years old
\therefore∴ Ram is 20 years old and Shyam is 28 years old.
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