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Algebra Level 1 Test 8

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Question 1
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 1 Explanation: 
Let the number of students in room A = a
Let the number of students in room B = b
Then
a – 10 = b + 10
a = b + 20
a + 20 = 2(b – 20)
From 1 and 2
b + 20 = 2a – 60
b = 80
a = 100
Question 2
If you subtract Rs. 1 from the money Bholu has, take its  reciprocal, then add it to the square of the money  and subtract the money Bholu has, you get two rupees more than the reciprocal of money after  subtracting 1 from it. Find the money Bholu has.
A
Rs.  7
B
Rs. 5
C
Rs. 10
D
None of these
Question 2 Explanation: 
Let money owned by Bholu = Rs. A
Therefore
{1/(A -1) + A2 – A} = 2 + 1/(A – 1)
A2 - A - 2 = 0
On solving
A = Rs. 2
Question 3
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 3 Explanation: 
Let the basic fare be Rs. a and reservation charges be Rs. b.
Then,
a+ b =216 ……………………………..1
(a + b)+ a/2 + b = 327
a/2 + b = 111…………………………..2
from 1 and 2
a = Rs. 210
Question 4
In a psychology school, the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Richa’s grade at the end of the first year is 40, what will be her grade at the end of the third year?
A
80
B
62
C
75
D
44
Question 4 Explanation: 
Richa’s grade at the end of first year = 40
Richa’s at the end of first year = 20
Richa’s grade at the end of second year
21 x 2 + 40/2 = 62
Richa’s grade at the end of third year
22 x 2 + 62/2 =75
Question 5
Some factory workers decided to have a party for their new comers at a total cost of Rs. 720. Four students decided to stay out of the party. To meet the expenses the remaining workers have to increase their share by Rs. 9. What is the original cost per worker?
A
18
B
36
C
40
D
39
Question 5 Explanation: 
Let original cost per worker be =Rs. a.
Therefore Total number of workers = 720
(720/a  - 4) x (a x 9)=720
=> 720 – 4a + 6480/a - 36 =720
=> a2 + 9a -1620 = 0
a = 36 and 45
so (b) is the right option
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