Question

In how many ways a batsman can score 200 with only 4's and 6's

Answer 1

4's(50)because 200÷4 is 50
6's(33.3)because 200÷4 is 33.3

Answer 2

Answer:

The answer is 17 ways

Step-by-step explanation:

Let the no. of 4's be x and 6's be y

So, the eqn. is 4x+6y=200

Simplifying the eqn we get 2x+3y=100

2x=100-3y

Since we know that for the number to be divisible by 2, unit digit should be even number.

So, this means that 100-3y should give an even number and for that 3y should also be an even number.

Therefore 3y will be even when y=0,2,4,6,...... ----> EQN 1

So now since 2x cannot be a fraction as well as a negative number so the last multiple of 3 that is less than 100 is 96

i.e., 3y=96

y=32

so, in EQN 1, the arithmetic progression or y value will go to 32

y= 0, 2, 4, 6.......32

So in this AP,

First term, a=0

Last term, l=32

common difference, d=2

l=a+(n-1)d

32=0+(n-1)2

16=n-1

n=17

So, in 17 ways the batsman can score a double century