Question

A sum of 3000 R.s is to be given in the form of 63 prizes. If the prize money is either 100 R.s or25 R.s. find the number of prizes of each type ​

Answer 1

Required Answer:-

Let's understand how to approach the solution first. We have certain number of Rs. 100 and Rs. 25 which add upto Rs. 3000. We will consider their numbers as some variables and find the total amount. Equating them will give our solution.

GiveN:

• Sum of money = Rs. 3000
• No. of prizes = 63
• The prize money is either of type Rs. 100/Rs. 25.

To Find the number of prizes of each type?

Let,

• No. of Rs. 100 note be x
• No. of Rs. 25 note be y.

Then,

According to question,

$\sf{ \longrightarrow{x + y = 63}}$

This is our equation (1)

Now the total amount contributed by Rs. 100 will be 100x and total amount contributed by Rs. 25 will be 25x. Then,

$\sf{ \longrightarrow{100x + 25y = 3000}}$

This is our equation (2)

Now multiplying 25 with equation (1).

$\sf{ \longrightarrow{25(x + y) = 1575}}$

$\sf{ \longrightarrow{25x + 25y = 1575}}$

Subtracting equation (1) from equation (2),

$\sf{ \longrightarrow{100x + 25y - (25x + 25y) = 3000 - 1575}}$

$\sf{ \longrightarrow{100x + 25y - 25x - 25y = 1425}}$

$\sf{ \longrightarrow{75x = 1425}}$

$\sf{ \longrightarrow{x = 19}}$

Then,

$\sf{ \longrightarrow{y = 63 - 19}}$

$\sf{ \longrightarrow{y = 44}}$

Hence:

• The total no. of Rs. 100 is 19
• The total no. of Rs. 25 is 44.

Answer 2

Given:-

➤A sum of 3000₹ is to be given in the form of 63 prizes .

➤The prize money is either 100 or 25₹

______________________

To Find:-

➤Find the number of prizes of each type ?...

_____________________________

Solution:-

✮First assume that all the 63 prizes are ₹25..

➤Total Amount = 25 × 63 = ₹1575

✮To Find the No of ₹100 prizes..

➤Difference in amount = 3000 - 1575 = ₹1425

➤The No of 100 ₹prize = Rupees 1425 ÷ (100 - 25) = 19

✮To Find the No of ₹25 prizes

➤The No of 100 ₹prize = 63 - 19 = 44

______________________

Hence:

✮19 - 100 ₹ Prizes.

✮44 - 25 ₹ Prizes.