R pays ₹100 to P with ₹5, ₹2 and ₹1 coins. The total number of coins used for paying are 40. What is the number of coins of denomination ₹5 in the payment?

Total payment = ₹100

Total number of coins = 40

Denominations used = ₹5, ₹2, ₹1 coins

Let number of ₹5 coins be x, number of ₹2 coins be y and number of ₹1 coins be z.

According to the question;

​$$x + y + z = 40 ….\tag{1}$$​​

and,

​$$5x + 2y + z = 100 …..\tag{2}$$​​

Now, subtracting (1) and (2)

​$$5x + 2y + z = 100 \\ \underline{-(x + y + z = 40) }\\ 4x + y \ \ \ = \ \ \ 60…. \tag{3}$$     

Now, 

    $$x =\frac{60 - y}{4} \\ \implies x = 15 - \frac{y}{4}$$   

So, the value of x should be less than 15 ,

Comparing from the option only option (d) 13 has value less than 15.

Therefore, option (d) 13 is correct.