Ayesha has only ₹ 5 and ₹ 10 coins with her. If the total number of coins she has is 25 and the amount of money with her is ₹ 160, then the number of ₹ 5 and ₹ 10 coins with her are

Correct Option: 18 and 7 respectively

Step-by-step Explanation:

Step 1: Define the variables
Let the number of ₹ 5 coins be represented by $x$.
Let the number of ₹ 10 coins be represented by $y$.

Step 2: Formulate the equations based on the given information
1. The total number of coins with Ayesha is 25.

$x+y=25$

(Equation 1)

2. The total amount of money with her is ₹ 160. The total value of ₹ 5 coins is $5x$ and the total value of ₹ 10 coins is $10y$.

$5x+10y=160$

(Equation 2)

Step 3: Solve the system of linear equations
From Equation 1, express $x$ in terms of $y$:

$x=25-y$

Substitute this expression for $x$ into Equation 2:

$5(25-y)+10y=160$

Expand and simplify the equation:

$125-5y+10y=160$

$125+5y=160$

Subtract 125 from both sides:

$5y=160-125$

$5y=35$

Divide by 5:

$y=7$

Now, substitute the value of $y$ back into $x=25-y$:

$x=25-7=18$

Conclusion:
Ayesha has 18 coins of ₹ 5 and 7 coins of ₹ 10 respectively.