Math Questions

August 16th, 2011 Posted in Uncategorized

Direction for next 3 Questions: Answer the Questions on the basis of the text given below.

There are 3 bottles and a jug. The bottles each have a capacity of 5 liters but are partially filled with water. The jug also has some water in it. The sum of the water in the jug and water in the first bottle is half of the total jug capacity. When the first bottle and third bottle are emptied into the jug, it contains 6 liters of water. When the second and the third bottle are emptied into the jug, it contains 7 liters of water. When all the bottles are poured into the jug, it’s filled to its capacity. The first and second bottles contain a total of 7 liters.

1. What percentage of total capacity of the bottles is filled with water?
a) 20% – 40%
b) 40% – 60%
c) 60% – 80%
d) 30% – 50%

2. What is the capacity of the jug? (In liters)
a) 7
b) 8
c) 9
d) 10

3. How much water does the jug already contain (in liters)?
a) 3
b) 4
c) 1
d) 2

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8 Responses to “Math Questions”

1. micky Says:

B
D
D

2. micky Says:

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3. vishnu Says:

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Congrats Micky!
all the best for the further rounds!

4. Uttam Says:

1. b
2. d
3. d

5. Uttam Says:

Explanation,
Say initially 3 bottles have x,y and z (First=x,y=second,z=third)
and jar has j.All are in liter.
Say jar capacity=m liter
So fror the question,
we get,
j+x=m/2—–(1)
x+z+j=6—–(2)
y+z+j=7—–(3)
x+y+z+j=m—-(4)
x+y=7—–(5)

By Equ3-equ2,
y-x=1—-(6)
From equ(5)and equ (6),
we get x=3 and y=4.
Putting x=3 and y=4 in equ 2 and equ 4, we get,
z+j=3 and z+j=m-7 so,m-7=3 or m=10,
so putting x=3 and m=10, in equ 1, we get,
j+3=10/2
or j=2
so z=3-j=3-2=1

so x+y+z=3+4+1=8
1. so the percentage of total capacity of the bottles is filled with water=(8/15)*100%=160/3% which is
approx 53.33% so ( 40% – 60%) is the write answer.

2.The capacity of the jug =M=10 L
3.The jug already contains j liter = 2 liter water .So answer is D.

6. Shreyasi Says:

b

d

d

I agree with Uttam’s solution. My equations are slightly different.

Answer to questions 1 to 3::
Let b1 stands for water in bottle 1, b2 stands for water in bottle 2 and b3 stands for water in bottle 3. and j stands for jug.

b1+ b3 + j = 6 … ( i )
b2+ b3 + j = 7 …( ii )
b1+ j = half jug … ( iii )
b1+ b2 + b3 + j = full jug … ( iv )
b1 + b2 = 7 … (v)
From (i), (ii) and (v), (ii) – (i) + (v)
2 b2 = 8, b2 = 4 Therefore, b1 = 3.
Also b3 + j = 3
Therefore, b1 + b2 + b3 + j = 7 + 3 = 10 = Full jug capacity
Thus we get all the values. Also b1 + j = 10/2 = 5
Therefore, b1 = 3, j = 5 – 3 = 2.
b3 = 3 – 2 = 1

1. b
(3 + 4 + 1) / 15 = 8/15 > 50%, hence b) 40% – 60%

2. d 10 liters

3. d 2 liters

8. uberVU - social comments Says:

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