A retired teacher donates Rs.5000 to the institution to be used as fiv

1.	A retired teacher donates Rs.5000 to the institution to be used as five cash prizes to Std.X students scoring highest marks in their overall academic performance. If each prize is Rs. 100 less than its preceding prize, find the value of each of the prizes.Please answer correct with explanation
Answer» Question :- A retired TEACHER donates Rs.5000 to the institution to be USED as five CASH prizes to Std.X students scoring highest marks in their overall academic performance. If each prize is Rs. 100 LESS than its preceding prize, FIND the value of each of the prizes. ? Solution :-- it is given that, the teacher donates Rs.5000 total between 5 students and each price is 100 less than the preceding prize . So, we can say that, the series is in AP, where sum of 5 numbers is 5000. we have now, → Total sum = 5000 → Number of terms = 5 → Common Difference = (-100) → Let First term = a . we know that, now, → sum of n terms of AP = n/2 [ 2a + (n-1)d ] Putting values now, we get, → 5000 = 5/2 [ 2a + (5-1)(-100) ] → 10002 = 2a - 400 → 2a = 2400 Dividing* both sides by 2 , → a = 1200 . So, First price is = Rs.1200 → 2nd price = 1200 - 100 = Rs.1100 → 3rd price = 1100 - 100 = Rs.1000 → 4th price = 1000 - 100 = Rs.900 → 5th price = 900-100 = Rs.800

A retired teacher donates Rs.5000 to the institution to be used as five cash prizes to Std.X students scoring highest marks in their overall academic performance. If each prize is Rs. 100 less than its preceding prize, find the value of each of the prizes.Please answer correct with explanation

Answer»

Question :- A retired TEACHER donates Rs.5000 to the institution to be USED as five CASH prizes to Std.X students scoring highest marks in their overall academic performance. If each prize is Rs. 100 LESS than its preceding prize, FIND the value of each of the prizes. ?

Solution :--

it is given that, the teacher donates Rs.5000 total between 5 students and each price is 100 less than the preceding prize .

So, we can say that, the series is in AP, where sum of 5 numbers is 5000.

we have now,

→ Total sum = 5000

→ Number of terms = 5

→ Common Difference = (-100)

→ Let First term = a .

we know that, now,

→ sum of n terms of AP = n/2 [ 2a + (n-1)d ]

Putting values now, we get,

→ 5000 = 5/2 [ 2a + (5-1)(-100) ]

→ 1000*2 = 2a - 400

→ 2a = 2400

Dividing both sides by 2 ,

→ a = 1200 .

So,

First price is = Rs.1200

→ 2nd price = 1200 - 100 = Rs.1100

→ 3rd price = 1100 - 100 = Rs.1000

→ 4th price = 1000 - 100 = Rs.900

→ 5th price = 900-100 = Rs.800