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Algebra: Linear Equation Test-2

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Question 1
Anil is at present one-fourth the age of his father. After 16 yr, he will be one-half age of his father. Find the present age of Anil's father.
A
40 yr
B
36 yr
C
32 yr
D
28 yr
Question 1 Explanation: 
Suppose present age of Anil is x & age of his father is y
Then acc. to question x=y/4.
After 16 years (x+16)=(y+16)/2
then x=8 & y=32.
Question 2
The electricity bill of a certain establishment is partly fixed and partly varies as the number of units of electricity consumed. When in a certain month 540 units are consumed, the bill is Rs.1800. In another month, 620 units are consumed and the bill is Rs.2040. In yet another month, 500 units are consumed. The bill for that month would be
A
Rs.1560
B
Rs.1680
C
Rs.1840
D
Rs.1950
Question 2 Explanation: 
Suppose fixed charge is Rs. p.
Electricity charge is Rs. y/unit.
Then p + 540y=1800
p + 620y=2040
Then y=3 & p= 180.
Now
Bill for 500 units would be: 180+500 x 3=1680
Question 3
Krishan has some hens and some cows. If the total number of animal heads is 59 and the total numbers of feet are 190, how many cows Krishan have?
A
36
B
32
C
23
D
Cannot be determined
Question 3 Explanation: 
Suppose no of hens are h
And numbers of cows are c
Then (h +c) =59
And 2c+4h=190
Then number of cows is 36
Question 4
The age of the father 5 yr ago was 5 times the age of his son. At present the father's age is 3 times that of his son. What is the present age of the father?
A
33 yr
B
30yr
C
45yr
D
None of these
Question 4 Explanation: 
 Let present age of son is x
Then present age of the father would be 3x.
5 years ago 3x-5=5(x-5)
ie x=10 then present age of the father will be 30 year.
Question 5
A lamp post has half of its length in mud, ⅓ of its length in water and 3⅓ m above the water. Find the total length of the post.
A
20 m
B
15 m
C
25 m
D
30 m
Question 5 Explanation: 
Suppose length of the lamp post is x.
Then length in water would be x-(x/2)-(x/3)=x/6
But it is equal to 3⅓ m
Therefore the value of x=20 m.
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