Question

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 1

Step-by-step explanation:

Let,

The number of two rupees coin be = x

So, no. of one rupee coins = 3x

Given,

Bag has amount of money as = Rs 150

Therefore, according to the problem,

=> Rs. 1 × 3x + Rs. 2 × x = Rs 150

=> 3x + 2x = 150

=> 5x = 150

$= > x = \frac{150}{5}$

=> x = 30

Required,

Number of two rupees coins = x = 30

Number of one rupee coins = 3x = 3 × 30 = 90

Conclusion, no. of one and two rupee coins are 30 and 90 respectively. (Ans)

Answer 2

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

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

• Total amount in bag is Rs 150.

$\large\underline{\bold{To\:Find - }}$

• 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

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

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.