Question 92

Bags I, II and III together have ten balls. If each bag contains at least one ball, how many balls does each bag have? Decide whether the data given in the statements are sufficient to answer the question.

Statement (1): Bag I contains five balls more than bag III.

Statement (2): Bag II contains half as many balls as bag I

Solution

Considering statement 1 alone,

Let the number of balls in bag III be x.

The number of balls in bag I becomes x+5.

And the rest, which is 10- (x+x+5)= 5-2x balls are with C.

We cannot find the value of x, so Statement 1 alone is not sufficient.

Considering statement 2 alone,ย

Let the number of balls in bag I be 2a

Balls in bag II will be a and the rest, i.e 10-3a will be in bag 3.

Again, we cannot find the value of a in this case, and hence, Statement 2 alone is not sufficient.

Considering both the statements and using the number of balls with each one of them as found using statement 1, we get

$$5+a=2\left(5-2a\right)$$

=>5+a= 10-4a

=> 5a=5, or a=1.

So, balls in Bag I= 5+a=6

balls in Bag II= 5-2a=3

balls in Bag III= a= 5.

Therefore, both statement I and II are required.

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