1.

In a bag, number of one rupee coin is three times than two rupees coin. If there are onlyRs 150 in this bag, then find out the number of both the coins​

Answer»

\large\underline{\bold{Given - }}

  • In a bag, number of one rupee coin is three times than two rupees coin.

  • Total AMOUNT in bag is Rs 150.

\large\underline{\bold{To\:<klux>FIND</klux> - }}

  • Number of coins of each type.

\large\underline{\bold{Concept \: Used-}}

Writing SYSTEMS of Linear Equation from Word Problem

Understand the problem.

  • Understand all the words used in stating the problem.

  • Understand what you are asked to find. ...

Translate the problem to an equation.

  • ASSIGN a variable (or variables) to represent the unknown.

  • Clearly state what the variable represents.

Carry out the plan and solve the problem.

\large\underline{\bold{Solution-}}

Given that

  • Number of one rupee coin is three times than two rupees coin.

\begin{gathered}\begin{gathered}\bf \: Let \: number \: of \: \begin{cases} &\sf{two \: rupee \: coin \: = \: x} \\ &\sf{one \: rupee \: coins = 3x} \end{cases}\end{gathered}\end{gathered}

So,

  • Value of 1 rupee coin in bag = 1 × 3x = 3x

and

  • Value of 2 rupees coin in bag = 2 × x = 2x

Now,

According to given statement,

Total amount is Rs 150 in the bag,

⇛ 2x + 3x = 150

⇛ 5x = 150

⇛ x = 30

\begin{gathered}\begin{gathered}\bf \: Hence \: number \: of \: \begin{cases} &\sf{two \: rupees \: coin \: = \: x = 30} \\ &\sf{one \: rupee \: coins = 3x = <klux>90</klux>} \end{cases}\end{gathered}\end{gathered}

Verification :-

Number of 2 rupees coin in bag = 30

Value of 2 rupees coin in bag = 2 × 30 = Rs 60

and

Number of 1 rupee coin in bag = 90

Value of 1 rupee coin in bag = 90 × 1 = Rs 90

So,

Total amount in bag = 90 + 60 = Rs 150

Hence, Verified.



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