1. Conversions
a. ( 11111000 )2=(?)10 b. (CD)16=(?)8
c. (11000011)2=(?)8 d. (200)10=(?)8
e. (D2)16=()2 f. (555)8=(?)2
g. (11111111)2=(?)16 h. (BB)16=(?)
Answers
Given:
The difference between present ages of Ram and Gaurav is 10 years.
After 5 years, Ram's is twice of Gaurav's age.
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To find:
Present age of Ram?
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☯ Let's Consider the present age of Ram and Gaurav be x and y years respectively.
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\begin{gathered}\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\\end{gathered}
★Accordingtothequestion:
The difference between present ages of Ram and Gaurav is 10 years.
\begin{gathered}:\implies\sf x - y = 10\\ \\\end{gathered}
:⟹x−y=10
\begin{gathered}:\implies\sf x = 10 + y\qquad\qquad\bigg\lgroup\bf eq\;(1) \bigg\rgroup\\ \\\end{gathered}
:⟹x=10+y
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eq(1)
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After 5 years, Ram's is twice of Gaurav's age.
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Their ages after 5 years,
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Age of Ram = (x + 5) years
Age of Gaurav = (y + 5) years
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Therefore,
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\begin{gathered}:\implies\sf (x + 5) = 2(y + 5)\\ \\\end{gathered}
:⟹(x+5)=2(y+5)
\begin{gathered}:\implies\sf x + 5 = 2y + 10\\ \\\end{gathered}
:⟹x+5=2y+10
\begin{gathered}:\implies\sf (10 + y) + 5 = 2y + 10\\ \\\end{gathered}
:⟹(10+y)+5=2y+10
\begin{gathered}:\implies\sf 15 + y = 2y + 10\\ \\\end{gathered}
:⟹15+y=2y+10
\begin{gathered}:\implies\sf y - 2y = 10 - 15\\ \\\end{gathered}
:⟹y−2y=10−15
\begin{gathered}:\implies\sf - y = - 5\\ \\\end{gathered}
:⟹−y=−5
\begin{gathered}:\implies{\underline{\boxed{\sf{\purple{y = 5}}}}}\;\bigstar\\ \\\end{gathered}
:⟹
y=5
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Now, Putting value of y in eq (1),
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\begin{gathered}:\implies\sf x = 10 + 5\\ \\\end{gathered}
:⟹x=10+5
\begin{gathered}:\implies{\underline{\boxed{\sf{\pink{x = 15}}}}}\;\bigstar\\ \\\end{gathered}
:⟹
x=15
★
Therefore,
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Present age of Ram, x = 15 years
Present age of Gaurav, y = 5 years