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Algebra: Linear Equation Test-1

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Question 1
Children had fallen-in for a drill. If each row contained 4 children less, 10 more rows would have been made. But if 5 more children were accommodated in each row the number of rows would have reduced by 5. The number of children in the school is
A
200
B
150
C
300
D
100
Question 1 Explanation: 
Suppose there are p rows & each row contains y no of children.
Then total no of children would be py.
Now according to question:  (p+10) (y-4) =py
=10y-4p=40……………………………………a
And (p-5) (y+5) = py.
5p -5y = 25
p – y =5………………………….b
After solving these two equations a and b, we get p=15 & y=10
Then total no of children would be 15 x 10=150
Question 2
There are two examination rooms A and B. If 10 candidates are sent from A to B, the number of students in each room is the same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. How many students are there in rooms A and B respectively?
A
100 and 80
B
120 and 60
C
80 and 100
D
140 and 60
Question 2 Explanation: 
Suppose there are x candidates in A and y candidates in B.
Then (x-10) = (y+10) ,
x = y +20…………………………..f
(x+20)=2(y-20)
x = 2y – 60………………………..g
After solving these two equation f and g we get x=100 & y=80
Question 3
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Sanchit paid Rs.45 for a book kept for 7 days, while Karan paid Rs.25 for the book he kept for 5 days. The fixed charge and the charge for each extra day is
A
Rs.5 and Rs.50
B
Rs.10 and Rs.5
C
Rs.15 and Rs.5
D
Rs.5 and Rs.15
Question 3 Explanation: 
Suppose fixed charge is x & additional charge for one day is y.
Then according to question (x+4y)=45
And (x+2y)=25. These 2 equations will give x=5 & y=10.
But in option b order has been changed.
Question 4
The basic one-way railway fare for a child aged between 3 and 10 yr costs half the regular fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult’s ticket. One reserved ticket for an adult costs Rs.216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs Rs.327. What is the basic fare for the journey for an adult?
A
Rs.210
B
Rs.52.50
C
Rs.111
D
Rs.58.50
Question 4 Explanation: 
Suppose basic fare for a child is Rs. x and basic fare for an adult is Rs. y.
Reservation charge is fixed for child, adult which is Rs. c .
Then according to equation
y +c=216
x+y+2c=327.
After solving these equations we get x=Rs. 105 and y=Rs. 210
Therefore the correct answer is option a
Question 5
One-fourth of Nikhil's money is equal to one-sixth of Yogesh's money. If both together have Rs.600, what is the difference between their amounts?
A
Rs.160
B
Rs.240
C
Rs.200
D
Rs.120
Question 5 Explanation: 
Suppose Nikhil has Rs. n and Yogesh has Rs. y
Then (n/4)=(y/6)
it is 3n=2y , both have 600 together ie. n +y=600
Then n=240 & y=360.
Difference would be Rs. 120
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