1.

Let Akbar and Birbal together have 'n' marbles, n>o.Akbar says to Birbal,"If I give you some marbles then you will have twice as many marbles as I will have."Birbal says to Akbar,"If I give you some marbles then you will have thrice as many marbles as I will have."What is the minimum possible value for 'n' for which the above statements are true?

Answer»

Final Answer:12

Step 1 :
Let Akbar and Birbal have 'a' and 'b' no. of Marbles.
Then,
according to the Question,
a + b = n ------------(1)

Step2:
Now,
Akbar gave 'x'(say) marbles to Birbal.
Then,
2(a-x) =(b+x)
=> 2a-b=3x ---------(2)

Step3:
Then,
Birbal gave 'y'(say) marbles to Akbar.
(a+y) = 3(b-y)
=>3b-a=4y------(3)

We have,
EQ. (2) and(3) ,
Finding a and b from both these EQUATIONS in terms of x and y.
we get,
a= (9x+4y)/5
b= (3x+8y)/5 .

Substituting value of a and b in equation 1.

a+b= n
=> n = 12(x+y)/5.

For 'n'to be the SMALLEST natural number.
x+y=5:
=> n = 12
----------------------------
Therefore, smallest value of n is 12.


Discussion

No Comment Found

Related InterviewSolutions