Question

A jar of liquid was left open and 1/8 of the liquid evaporated the first day, 1/6 of the remainder evaporated the 2nd day, and 1/2 of the remainder the 3rd day. What fractional part of the original amount was left after the 3rd day

Answer 1

Given : A jar of liquid evaporated $\dfrac{1}{8}$ of liquid on first day, $\dfrac{1}{6}$ of the remaining on the second day and $\dfrac{1}{2}$ of the remaining on the third day.

To Find : Fractional part of remaining liquid in the jar with respect to the original quantity of the liquid after the third day.

Solution :

As 8, 6, 2 is given in the denominator part of the fractional part in which the liquid evaporated.

∴ Let the original quantity of the liquid in the jar = 8×6×2 = 96 unit.

Now, the liquid evaporated on first day =  $\dfrac{1}{8}$  of 96 =  $\dfrac{1}{8}$ × 96 = 12 unit

∴ liquid remained in the jar after first day = 96 - 12 = 84 unit

Again, the liquid evaporated on 2nd day =  $\dfrac{1}{6}$ of 84 = $\dfrac{1}{6}$ × 84 = 14 unit

∴  liquid remained in the jar after 2nd day = 84 - 14 = 70 unit

And, again liquid evaporated on 3rd day =  $\dfrac{1}{2}$  of 70 =  $\dfrac{1}{2}$  × 70 = 35 unit

∴  liquid remained in the jar after 3rd day = 70 - 35 = 35 unit.

∴ fractional part of the liquid left in the jar = $\dfrac{remaining}{original}$ = $\dfrac{35}{96}$

So,  $\dfrac{35}{96}$ amount of liquid was left in the jar after the 3rd day.