Rajeev donated a sum of ₹700000 to a school from his life long saving by given seven cash prizes to students for their over all academic performance. If each prizes is ₹20000 less than it's preceding prizes. Find the value of each of the prizes. What value is depicted from his action.
Answers
Cost of 2nd prize = a − 20000
Cost of 3rd prize = a− 40000
Cost of these prizes are in an A.P. having common difference(d) as −20000 and first term as a.
First term= a
d = −20000
Given that, S7 = 700000
7/2 [2a + (7 - 1)d] = 700000
]Sn = n/2{2a+(n-1)d}]
7/2[2a +6d] = 700000
7[2a +6d] = 700000×2
14a + 42d = 1400000
7[2a +6d] = 1400000
7× 2[a+3d] = 1400000
14[a+3d] = 1400000
a+3d = 1400000/14
a+3d =100000
a + 3(−20000) = 100000
a − 60000 = 100000
a= 100000+60000
a = 160000
Hence, the value of each of the prizes was ₹160000, ₹140000, ₹120000, ₹10000,₹ 80000, ₹ 60000, & ₹ 40000.
Value depicted from this action is :
Helping students of the country and promoting educational standards
HOPE THIS WILL HELP YOU....
The total amount donated = Rs.7,00,000.Let the first prize be Rs.x. Each prize is Rs.20,000 less than the preceeding prize.
Then,
The second prize is x - 20,000
The third prize is (x - 20,000) - 20,000 = x - 40,000
The fourth prize is (x - 40,000) - 20,000 = x - 60,000
The fifth prize is (x - 60,000) - 20,000 = x - 80,000
The sixth prize is (x - 80,000) - 20,000 = x - 1,00,000
The seventh prize is (x - 1,00,000) - 20,000 = x - 1,20,000
Hence,
x + (x - 20,000) + (x - 40,000) + (x - 60,000) + (x - 80,000) + (x - 1,00,000) + (x - 1,20,000) = 7,00,000
=>7x - 4,20,000 = 7,00,000
=>7x = 11,20,000
=>x = 1,60,000 (First prize is Rs.1,60,000)
Second prize is x - 20,000 = 1,60,000 – 20,000 = Rs.1,40,000
Third prize is x - 40,000 = 1,60,000 – 40,000 = Rs.1,20,000
Fourth prize is x - 80,000 = 1,60,000 – 60,000 = Rs.1,00,000
Fifth prize is x - 80,000 = 1,60,000 – 80,000 = Rs.80,000
Sixth prize is x - 1,00,000 = 1,60,000 – 1,00,000 = Rs.60,000
Seventh prize is x - 1,20,000 = 1,60,000 – 1,20,000 = Rs.40,000
Value depicted from this action is that Rajeev encourages children to study well and come up in life.