Question

Six years ago, the ratio of the ages of Ram and Shyam was 6:5. Four years in future from today the ratio of their ages will be 11:10, what is Shyam's present age?​

Answer 1

Answer:-

$\red{\bigstar}$ Shyam's present age $\large\leadsto\boxed{\rm\green{16 \: years}}$

• Given:-

Six years ago, the ratio of the ages of Ram and Shyam was 6:5.

Four years in future from today the ratio of their ages will be 11:10.

• To Find:-

The present age of Shyam.

• Solution:-

Let the present ages of Ram be 'x' and Shyam be 'y'.

• According to the question:-

✴ Six years ago ratio of Ram and Shyam's age was 6:5.

→ $\\ \sf \dfrac{x-6}{y-6} = \dfrac{6}{5}$

→ $\sf 5(x-6) = 6(y-6)$

→ $\sf 5x - 30 = 6y - 36$

→ $\sf 5x - 6y - 30 + 36 = 0$

→ $\sf 5x - 6y + 6 = 0$

→ $\bf 5x - 6y = -6 \dashrightarrow\bf\red{[eqn.i]}$

Now,

✴ Four years in future the ratio will be 11:10.

→ $\\ \sf \dfrac{x+4}{y+4} = \dfrac{11}{10}$

→ $\sf 10(x+4) = 11(y+4)$

→ $\sf 10x + 40 = 11y + 44$

→ $\sf 10x - 11y + 40 - 44 = 0$

→ $\sf 10x - 11y - 4 = 0$

→ $\sf 10x - 11y = 4 \dashrightarrow\bf\red{[eqn.ii]}$

• Multiplying eqn[i] by 2:-

→ $\sf 5x - 6y = -6$

→ $\sf (5x - 6y = -6) \times 2$

→ $\bf 10x - 12y = -12 \dashrightarrow\bf\red{[eqn.iii]}$

• Subtracting eqn[iii] from [ii]:-

→ $\sf (10x - 11y) - (10x - 12y) = 4 - (-12)$

→ $\sf 10x - 11y - 10x + 12y = 4 + 12$

★ $\large{\bf\pink{y = 16}}$

• Substituting the value of y in eqn[i]:-

→ $\sf 5x - 6y = -6$

→ $\sf 5x - 6 \times 16 = -6$

→ $\sf 5x - 96 + 6 = 0$

→ $\sf 5x - 90 = 0$

→ $\sf 5x = 90$

→ $\sf x = \dfrac{90}{5}$

★ $\large{\bf\pink{x = 18}}$

Therefore, the present ages of

Ram = 18 years

Shyam = 16 years

Answer 2

Answer:

Answer:-\red{\bigstar★Shyam'spresentage\larges

• Given:-

Six years ago, the ratio of the ages of Ram and Shyam was 6:5.

Four years in future from today the ratio of their ages will be 11:10.

• To Find:-

The present age of Shyam.

• Solution:-

Let the present ages of Ram be 'x' and Shyam be 'y'.

• According to the question:-

✴ Six years ago ratio of Ram and Shyam's age was 6:5.

→\begin{gathered\sf\dfrac{x-6{y-6=\dfrac{6{5}\e{x−6}

= 56

→ \sf 5(x-6) = 6(y-6)5(x−6)=6(y−6)

→ \sf 5x - 30 = 6y - 365x−30=6y−36

→ \sf 5x - 6y - 30 + 36 = 05x−6y−30+36=0

→ \sf 5x - 6y + 6 = 05x−6y+6=0

→ \begin{gathered}\bf 5x - 6y = -6 \dashrightar\bfed{[eqn.i\end{gathered5x−6y=−6⇢[eqn.i]

Now,

✴ Four years in future the ratio will be 11:10.

→\begin{gathered\sf\dfrac{x+4{y+4=\dfrac{11{10\e4

= 1011

→ \sf 10(x+4) = 11(y+4)10(x+4)=11(y+4)

→ \sf 10x + 40 = 11y + 4410x+40=11y+44

→ \sf 10x - 11y + 40 - 44 = 010x−11y+40−44=0

→ \sf 10x - 11y - 4 = 010x−11y−4=0

→ \begin{gathered}\sf 10x - 11y = 4 \dashrightarrow\bf\red{[eqn.ii]} \\ \end{gathered}

10x−11y=4⇢[eqn.ii]

• Multiplying eqn[i] by 2:-

→ \sf 5x - 6y = -65x−6y=−6

→ \sf (5x - 6y = -6) \times 2(5x−6y=−6)×2

→ \begin{gathered}\bf 10x - 12y = -12 \dashrightarrow\bf\red{[eqn.iii]} \\ \end{gathered}

10x−12y=−12⇢[eqn.iii]

• Subtracting eqn[iii] from [ii]:-

→ \sf (10x - 11y) - (10x - 12y) = 4 - (-12)(10x−11y)−(10x−12y)=4−(−12)

→ \sf 10x - 11y - 10x + 12y = 4 + 1210x−11y−10x+12y=4+12

★ \begin{gathered}\large{\bf\pink{y = 16}} \\ \end{gathered}

y=16

• Substituting the value of y in eqn[i]:-

→ \sf 5x - 6y = -65x−6y=−6

→ \sf 5x - 6 \times 16 = -65x−6×16=−6

→ \sf 5x - 96 + 6 = 05x−96+6=0

→ \sf 5x - 90 = 05x−90=0

→ \sf 5x = 905x=90

→ \sf x=\dfrac{90{5x=590★\large{\bf\pink{x=18x=18

Therefore, the present ages of

Ram = 18 years

Shyam = 16 years