Advertisements
Advertisements
प्रश्न
In a cricket team tournament 16 teams participated. A sum of ₹8000 is to be awarded among themselves as prize money. If the last place team is awarded ₹275 in prize money and the award increases by the same amount for successive finishing places, then how much amount will the first place team receive?
Advertisements
उत्तर
We have,
the total sum of prize money to be awarded among 16 teams, S16 = ₹8000 and
the prize money awarded to the last place team i.e. a16 = ₹275
As, the award increases by the same amount for successive finishing places.
So, the prize money are in A.P.
Let the prize money awarded to the first team be a.
Now,
\[S_{16} = 8000\]
\[ \Rightarrow \frac{16}{2}\left[ a + a_{16} \right] = 8000\]
\[ \Rightarrow 8\left[ a + 275 \right] = 8000\]
\[ \Rightarrow a + 275 = \frac{8000}{8}\]
\[ \Rightarrow a = 1000 - 275\]
\[ \therefore a = 725\]
So, the amount which the first place team will recieve is ₹725.
संबंधित प्रश्न
Find the sum to n terms of the A.P., whose kth term is 5k + 1.
The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that the ratio of mth and nthterm is (2m – 1): (2n – 1)
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
if `a(1/b + 1/c), b(1/c+1/a), c(1/a+1/b)` are in A.P., prove that a, b, c are in A.P.
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will be the tractor cost him?
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]
The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.
Is 68 a term of the A.P. 7, 10, 13, ...?
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
Find the 12th term from the following arithmetic progression:
3, 5, 7, 9, ... 201
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.
If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of the following serie:
(a − b)2 + (a2 + b2) + (a + b)2 + ... + [(a + b)2 + 6ab]
Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
Find the sum of all even integers between 101 and 999.
Solve:
1 + 4 + 7 + 10 + ... + x = 590.
Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.
If the sum of n terms of an A.P. is nP + \[\frac{1}{2}\] n (n − 1) Q, where P and Q are constants, find the common difference.
If a2, b2, c2 are in A.P., prove that \[\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}\] are in A.P.
If a, b, c is in A.P., then show that:
b + c − a, c + a − b, a + b − c are in A.P.
Show that x2 + xy + y2, z2 + zx + x2 and y2 + yz + z2 are consecutive terms of an A.P., if x, y and z are in A.P.
There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount. How much the scooter will cost him.
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
A man saved ₹66000 in 20 years. In each succeeding year after the first year he saved ₹200 more than what he saved in the previous year. How much did he save in the first year?
If \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 7, then find the value of n.
If a, b, c are in G.P. and a1/x = b1/y = c1/z, then xyz are in
Find the sum of first 24 terms of the A.P. a1, a2, a3, ... if it is known that a1 + a5 + a10 + a15 + a20 + a24 = 225.
Show that (x2 + xy + y2), (z2 + xz + x2) and (y2 + yz + z2) are consecutive terms of an A.P., if x, y and z are in A.P.
A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. Find his salary for the tenth month
If the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of p + q terms is – (p + q). Also, find the sum of first p – q terms (p > q).
