bowl - half full of water

bhumika.k.shah wrote:A bowl was half full of water.4 cups of water were then added o the bowl, filling the bowl to 70% of its capacity.How many cups of water are now in the bowl ?

[spoiler]Source : MGMAT fractions book
OA : 14[/spoiler]

What are the different approaches possible here ?

My approach,

20 % = 4 cups

100 % = 20 cups

70% = 14 cups [spoiler]( hardly 10 secs I think )[/spoiler]

bhumika.k.shah wrote:A bowl was half full of water.4 cups of water were then added o the bowl, filling the bowl to 70% of its capacity.How many cups of water are now in the bowl ?

[spoiler]Source : MGMAT fractions book
OA : 14[/spoiler]

What are the different approaches possible here ?

If 4 cups are equivalent to 20 percent, then 70 percent is equivalent to 4/20 × 70 = 14 cups.

But how are 4 cups equivalent to 20% ?
where is this mentioned in the sum ?

bhumika.k.shah wrote:But how are 4 cups equivalent to 20% ?
where is this mentioned in the sum ?

The bowl was already half full of water, half bole toh pachaas taka, half is taken as 50 percent in mathematics. This becoming 70 percent means 20 percent of the total volume is what has been added to it.

4 cups is 20% of bowl
therefore 1 cup fills 5 % of the bowl.
5 is a easy figure when dealing with figures like 20, 70 100 %

bhumika.k.shah wrote:But how are 4 cups equivalent to 20% ?
where is this mentioned in the sum ?

A bowl was half full of water.4 cups of water were then added o the bowl, filling the bowl to 70% of its capacity.How many cups of water are now in the bowl ?


What are the different approaches possible here ?

Hey bhumika,
Lets look at it step by step by looking at the wording of the sentence.
1) A bowl was half full of water – This implies 50% capacity of bowl was filled.
2) 4 cups of water were then added to the bowl, filling the bowl to 70% – Now,the bowl becomes 70% filled.
3) Subtracting the bowl capacity in step 1 from bowl capacity in step 2,we get 20% capacity.
4)Now,we know that this 20% capacity was filled by 4 cups.Hence,4 cups = 20%
5)Multiplying by 5,we get 20 cups =100%
6)Now,bowl is filled upto 70% which is (70/100) x 20 = 14 cups which is the answer.

If you have problem regarding such shortcut techniques,I think it is better to go through Word Translations and know how the question setter hides the shortcuts in the wording of the sentence.

I hope the above illustration helps.

bhumika.k.shah wrote:A bowl was half full of water.4 cups of water were then added o the bowl, filling the bowl to 70% of its capacity.How many cups of water are now in the bowl ?

[spoiler]Source : MGMAT fractions book
OA : 14[/spoiler]

What are the different approaches possible here ?

since 4 cups of water changes the capacity from 50% to 70%. hence 1 cup corresponds to 5%
hence no.of cups of water = 70/5 = 14 Ans ( 10 sec question)

bhumika.k.shah wrote:A bowl was half full of water.4 cups of water were then added o the bowl, filling the bowl to 70% of its capacity.How many cups of water are now in the bowl ?

[spoiler]Source : MGMAT fractions book
OA : 14[/spoiler]

What are the different approaches possible here ?

let capacity of bowl=c

50% filled=c/2
let capacity of each cup=x
total amnt of cups added=4x

after addition 4x bowl contains=4x+c/2
which is=70% of full=7/10 of c

so 4x=7c/10 - c/2
or x=c/20

# of cups in the bowl=[7c/10]/[c/20]=14