Question

there are 21 balls of different colors in a box. if the number of balls of each color is a consecutive number starting from one, how many different colors are available in the box?




a. 4
b. 5
c. 6
d. 7
​

Answer 1

Answer:

6

Step-by-step explanation:

Because when you start from 1 it goes like

1+2+3+4+5+6= 21

so of there are 21 balls which are numbered in consecutive starting from 1 so the answer should be 6

I hope this helps you

thank you

Answer 2

6 colours are available in the box.

Given : There are 21 balls of different colours in a box. if the number of balls of each colour is a consecutive number starting from one.

To find : Number of colours.

Solution :

We can simply solve this mathematical problem by using the following mathematical process.

Here, we will be using AP series formula.

In this case,

• First term AP (a) = 1 [As, we start from 1]
• Common difference (d) = 1 [As, the numbers are consecutive.]
• Number of terms (n) = ? (unknown quantity) [n means number of available colours]
• Sum of terms (Sn) = 21 [Sn means total balls]

So,

Sn = (n/2) × [2a + (n-1) × d]

By, putting the available data, we get :

21 = (n/2) × [(2×1) + (n-1) × 1]

21 = (n/2) × (2+n-1)

21 = (n²+n)/2

42 = n²+n

n²+n-42 = 0

n²+7n-6n-42 = 0

n(n+7) - 6(n+7) = 0

(n-6) (n+7) = 0

Either,

n-6 = 0

n = 6

Or,

n+7 = 0

n = -7

Now, number of terms (n) cannot be negative. So, we will omit, n = -7

So, n = number of colours = 6

Hence, 6 colours are available in the box.