#Algebra
Practice Examples 1, Practice Examples 2
Q.1
A test is conducted in class X of 10 students. The scores are 11, 15, 18, 14, 15, 15, 11, 9, and 16. If Albert scored 2 more than the average of all the students, what is the score of Albert?
A. 9
B. 12
C. 14
D. 16
E. 15
Answer
If we observe the data we find that the score is given for 9 students out of 10 students.
10 x a = 126+ a
10a = 126 + a
Transpose ‘a’ to left side or subtract ‘a’ from both side
10a – a = 126
9a = 126
a = 126/9
a = 14
So, average score of all the students is 14 and Albert’s score is 2 more than average that means Albert’s score is 14 + 2 =16.
The answer is ‘D’.
Q.2
In a book shop Geography books are half of Math books and Math book are double of English Books. There are 250 English books.
Quantity A Quantity B
Geography Books 250
A. If Quantity A is greater
B. If Quantity B is greater
C. If Quantity A and Quantity B are equal
D. The relationship cannot be determined from given information
Solution
First we take Math books = m, Geography books = g and English books = e
g = m/2 ……………. Equation 1
m = 2 x e …………………..Equation 2
Put the value of Equation 2 in Equation 1
g = 2 x e /2
g = e
Numbers of English Books = 250 so there will be same numbers of Geography books.
g = e = 250
If we compare Quantity A with Quantity B, the value for both is same,
Hence, the answer is ‘C’.
Q.3
Ronnie walks to school at a rate of 8miles per hour every day. If he walks doubles to his daily rate, how much time he will take to cover the distance of 16 miles?
A. 15 min.
B. 60 min.
C. 40 min.
D. 120 min.
E. 30 min.
Solution;
Distance = rate x time
Rate = 8 miles per hour
Distance = 16 miles, Time =?
Ronnie walks doubles to his daily rate i.e. = 2 x R = 2 x 8 = 16 miles per hour
Time ‘T’ = Distance / Rate
= 16/16
= 1 Hour
= 60 minutes
The answer is ‘B’.
Q.4
Albert drives a car at an average speed of 72 miles per hour to reach at station B from station ‘A’ in 36 minutes. How much time John will take if he drives the car at an average speed of 81 miles per hour to reach at station B from station A?
A. 16 min.
B. 20 min.
C. 35 min.
D. 40 min.
E. 32 min.
Solution;
Hint; Here the distance is same for both Albert and John.
Let us take Albert’s speed = r1 = 72 miles per hour, time = t1 = 36 minutes
Distance traveled by Albert = d1 = r1 x t1
= 72 x 36
Now, John’s Speed = r2 = 81 miles per hour, time = t2 =?
Distance travelled by John = d2 = r2 x t2
= 81 x t2
Distance travelled by Albert and John is same so, d1 = d2
72 x 36 = 81 x t2
t2 = (72 x 36) / 81
t2 = 32 minutes
The answer is ‘E’.
Q.5
Alia and Albert start running from point ‘A’ in opposite direction. If Alia runs at 3 miles per hour slower than Albert and after 5 hours they are 25 miles apart. Find the rate at which Alia was running?
Solution;
Hint; Here both are running in opposite direction so add the distance.
Albert’s Rate = r1, distance = d1, time = t1=5; d1 = r1 x t1 = r1 x 5
Alia’s Rate = r2, distance = d2, time = t2=5; d2 = r2 x t2 = r2 x 5
Alia’s runs at 3miles/hour lower than Albert i.e.; r2 = r1- 3………….Equation 1
After 5 hours they are 25 miles apart
d1 + d2 = 25
r1 x 5 + r2 x 5 = 25
r1 x 5 + (r1-3) x 5 = 25 …………..from equation 1
5r1 + 5r1 – 15 = 25
10 r1 = 25 +15
10r1 = 40
r1 = 40/10
r1 = 4 miles per hour
Albert’s rate ‘r1’ = 4 miles per hour
Alia’s rate r2 = r1 – 3
= 4 – 3
Alia’s rate = 1 miles per hour
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