Problem Solving

Hi there,

Could you give me your ELEGANT, QUICK, and EFFICIENT method to resolve (with these concepts and with finding the solution).


Equal amounts of water were poured into two empty jars of different capacities, which made one jar ¼ full
and the other jar 1/3 full. If the water in the jar with the lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?

a)1/7
b)2/7
c)½
d)7/12
e)2/3

I find picking numbers easiest on this question:

jar with capacity of 9 liters and
jar with capacity of 12 liters.

Pour 3 liters into each of them (smaller one: 3/9=1/3; bigger one: 3/12=1/4).
Now pour the 3 liters of the smaller jar into the bigger one and you get 6/12=1/2

Answer C (1/2)

many thks

OA is C

Some of these questions are best with numbers picked.


Jar A: Capacity = 12 litres
A: 1/4 * 12 = 3 litres

Jar B: We need to use the same amount so we set x(capacity of B) to 3 litres.

1/3 * x = 3 litres
x = 9 litres
Jar B: 9 litres

3 litres + 3 litres = 6 litres
6/12 = 1/2
C

Xbond wrote:Hi there,

Could you give me your ELEGANT, QUICK, and EFFICIENT method to resolve (with these concepts and with finding the solution).


Equal amounts of water were poured into two empty jars of different capacities, which made one jar ¼ full
and the other jar 1/3 full. If the water in the jar with the lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?

a)1/7
b)2/7
c)½
d)7/12
e)2/3

1/4 A = 1/3 B
A' = 1/4A + 1/3B
So A' = 1/4A + 1/4A = 1/2A

Thanks

lets assume, that amount of water= 1

then-

1=1/3*C1 (C1=Capacity of jar 1) C=3

1=1/4*C2 C2=4

from above info, we can easily assume that jar 1 is with lesser capacity. so, we add the amount of water of jar 1 to the amount of water of jar 2.

now we have (1+1)/4 =1/2

once more
x and y are two jars
x/4=y/3 and 4y=3x. It's evident y is less than x. Therefore, (y/3+x/4)/x will give us right proportion. We need to substitute and plug in y=3x/4 -> (3x/12+x/4)/x=6x/12x=1/2