Question

a sum of Rs1890 is to be used to give seven cash prizes. If each prize is Rs 50 less than the preceeding prize, find the value of each prize

Answer 1

There are 7 Prizes

Let the Prize money of First Prize be x

∴ Prize Money for all Seven Prizes be like

x, x - 50, x - 100, x - 150, .... (∵ Each Prize is 50 less than the preceding prize)

Here we can see the difference between two consecutive terms is equal

Which is - 50

So we can say the prize money forms an AP with

first term (a) = x

Common difference (d) = -50 and

number of terms (n)  = 7

Here you can observe that the Sum of all 7 Prizes is 1890

$S_{n} = 1890$

But we know that in an AP

$S_n = \frac{n}{2}[2a + (n-1)d]$

Putting Values

$1890 = \frac{7}{2}[2x + (7-1)(-50)]\\\</p><p>frac{2}{7} \times 1890=[2x -300]$

540 = 2x - 300

2x = 840

x = 420

Hence Prize Money for 7 Prize is

420, 370, 320, 270, 220, 170, 120