Question

Find the sum of two numbers which are in the ratio 3:5 and their sum is 196.​

Answer 1

$\large\underline{ \underline{ \sf \maltese\red{ \: Correct \: Question:- }}}$

• Find the sum of two numbers which are in the ratio 3:4 and their sum is 196.

$\large\underline{ \underline{ \sf \maltese\red{ \: Solution:- }}}$

• Let the First Number be 3x
• Let the Second Number be 4x
• Their sum is 196

$\begin{gathered}\begin{gathered}\underline{\boldsymbol{According\: to \:the\: Question :}} \\\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{3x \: + \: 4x \: = \: 196 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 7x \: = \: 196 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{x \: = \: \frac{196}{7} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{x \: = \: \cancel \frac{196}{7} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{x \: = \: 28 }}}$

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$\large\underline{ \underline{ \sf \maltese\red{ \: Verification:- }}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{3x \: + \: 4x \: = \: 196 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{3 \times 28 \: + \: 4 \times 28\: = \: 196 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 84 \: + \: 112\: = \: 196 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{196\: = \: 196}}}$

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• First Number = 3x = 3 × 28 = 84
• Second Number = 4x = 4 × 28 = 112

$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ First \: Number \: = \underline {\underline{ 84}}}\\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Second\: Number \: = \underline {\underline{ 112}}}\\\end{gathered}\end{gathered}$

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More For Knowledge:-

$\underbrace\red{\boxed{ \sf \blue{ Steps \: to \: Solve \: a \: Word \: Problem}}}$

1. Step 1 :- Read the problem carefully and find out what is given and what is to be determined.
2. Step 2 :- Represent the unknown quantity by a variable like x , y , z , etc.
3. Step 3 :- Form a linear equation with the help of the given condition.
4. Step 4 :- Solve the equation as usual.
5. Step 5 :- To be very sure , you may verify your answer.

Tips and Tricks:-

The Solution of word problems can be verified by placing the value of variables in the obtained equation.

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Answer 2

• Let the First Number be 3x
• Let the Second Number be 4x
• Their sum is 196

According to the question:-

3x + 4x = 196

7x = 196

x = 196/7

x = 28

Then,

3 × 28 = 84

4 × 28 = 112

Therefore , First number is 84 and second number is 112