CHAPTER:1-IMP SUMS

Q. If A gives 1/6th part of the amount with him to B, the Amounts with both becomes equal. If B gives Rs.16 to A, then A's Amount becomes two and a half that with B. Find the amount with each.

ANS. Let the amount with A be Rs.x and the amount with B be Rs.y.

According to the First Condition,
x-x/6 = y+x/6
Therefore, (6x-x)/6 = (6y+x)/6
Therefore, 6x-x = 6y+x
Therefore, 6x-x-6y-x = 0
Therefore, 6x-6y-2x = 0
Therefore, 4x-6y = 0 ...........................eq.1

According to the Second Condition,
x+16 = 5/2 (y-16)
Therefore, 2x+32 = 5y-80
Therefore, 2x-5y = -80-32
Therefore, 2x-5y = -112......................eq.2

Multiplying eq.1 by 2, and then eliminating(subtarction),

We Get...4y = 224
Therefore, y = 224/4
Therefore, y = 56

Putting y=56 in eq.1, we get...

4x-6y=0
Therefore, 4x-6(56)=0
Therefore, 4x-336=0
Therefore, 4x=336
Therefore, x=336/4
Therefore, x=84

ANS: The Amount with A is Rs.84 and The Amount with B is Rs.56