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.
Please answer correct with explanation ​

Answer 1

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

Answer 2

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➠ Given

• Sum of terms (Sn) = 5000
• First term (a) = ?
• Common Difference (d) = -100
• Number of terms (n) = 5

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➠ To Find

• First term (a)

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➠ Solution

We have formula for Sum of terms :

$\large \star {\boxed{\sf{S_n \: = \: \dfrac{n}{2} \bigg( 2a \: + \: (n \: - \: 1) d\bigg)}}} \\ \\ \\ \implies {\sf{5000 \: = \: \dfrac{5}{2} \bigg( 2a \: + \: (5 \: - \: 1)-100 \bigg)}} \\ \\ \\ \implies {\sf{5000 \: = \: \dfrac{5}{2} \bigg( 2a \: + \: (4)-100 \bigg)}} \\ \\ \\ \implies {\sf{\dfrac{5000 \: \times \: 2}{5} \: = \: 2a \: - \: 400}} \\ \\ \\ \implies {\sf{1000 \: \times \: 2 \: = \: 2a \: - \: 400}} \\ \\ \\ \implies {\sf{2000 \: = \: 2a \: - \: 400}} \\ \\ \\ \implies {\sf{2a \: = \: 2000 \: + \: 400}} \\ \\ \\ \implies {\sf{2a \: = \: 2400}} \\ \\ \\ \implies {\sf{a \: = \: \dfrac{2400}{2}}} \\ \\ \\ \implies {\sf{a \: = \: 1200}}$

$\therefore$First Term is 1200

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➠ a1 = Rs.1200

➠ a2 = a1 - d = Rs. 1100

➠ a3 = a2 - d = Rs. 1000

➠ a4 = a3 - d = Rs. 900

➠ a5 = a4 - d = Rs. 800