# Arithmetic
Q.1 www.limaglobal.com
In a class there are boys and girls in a ratio of 8:5. If 40 boys are there in the class, how many are the girls?
A. 15
B. 20
C. 30
D. 25
E. 28
Answer:
The ratio of boys to girls is 8 : 5
(Boys/Girls) =( 8/5)
There are 40 boys; So, Girls = 40 x (5 /8)
Girls = 25
The correct answer is ‘D’.
Lima Global Institute of Virtual Learning
Q.2 www.limaglobal.com
If 30% of ‘m’ is equal to three fourth of ‘n’
Quantity A Quantity B
n/m 2:5
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;
30% of m = (30/100) x m = (3/4) of n
n/m = (4 x 30)/ (3 x 100)
n/m = 2/5
Or n/m = 2:5
If we compare Quantity A with Quantity B, both are equal, hence, the correct answer is ‘C’.
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Lima Global Institute of Virtual Learning
Q.3 www.limaglobal.com
In a shopping mall men are one fourth of women and the numbers of children and women are in ratio of 1:2. If there are total 350 people including men and women and children, how many of them are men and children?
A. 150
B. 50
C. 200
D. 225
E. 175
Solution
Let us take men = m, women = w and children = c
Men are one fourth of women i.e. m = ¼ w
The ratio of children to women = c/w = ½ i.e. ‘c’ = ½ w
Total people in the shopping mall;
Men + women+ children = 350
¼ w + w + ½ w = 350
Solve the equation by taking LCM
(W + 4W + 2W)/4 = 350
Multiply both sides by 4
7w = 350 x 4
w = 50 x 4
w = 200
There are 200 women in the shopping mall.
Men = ¼ w = ¼ x 200 = 50
Children = ½ w = ½ x 200 = 100
The numbers of men and children are = 50 +100 = 150
The correct answer is ‘A’.
Lima Global Institute of Virtual Learning
Q.4 www.limaglobal.com
In a forest tigers and bears are in the ratio of 2:3. If 25% tigers and 50% bears come from another forest, find the new ratio?
A. 2:5
B. 5: 9
C. 3:6
D. 5:8
E. 9:5
Solution;
Let us take that there are ‘m’ numbers of tigers and bears
Tigers = 5m and bears = 6m, Some tigers and bears come from another forest
There is 25% increase in tigers that is = 125%
And 30% increase in bears = 130%
Percent increase
New ratio of tigers to bears will be 5:9.
The answer is ‘B’.
Quantity A is 2/3 and Quantity B is 1/3. Quantity B which is lesser than Quantity A.
The answer is ‘A’.
Q.6 www.limaglobal.com
In a class of 35 boys and girls, which of the following could be the ratio of boys to girls?
A. 1: 4
B. 2: 5
C. 1: 8
D. 1: 7
E. 6: 1
Answer:
In this type of sum total ratio should be multiple of the number given, as it is not possible for any fractional value for the number of boys and girls.
Here, total 35 boys and girls are in a class.
Take the option choices one by one
Choice ‘A’; Addition of ratio 1: 4 = 5 which is a multiple of 35, means there could be (1/5) x 35 = 7 boys and (4/5) x 35 = 28 girls.
Choice ‘B’; Addition of ratio 2:5 = 7, multiple of 35,
(2/7) x 35 = 10 boys, (5/7) x 35 = 25 girls
Choice ‘C’; Addition of ratio 1: 8 = 9, not a multiple of 35, resultant will be fraction number which is not possible.
Choice ‘D’; Addition of ratio 1: 7 = 8, not a multiple of 35
Choice ‘E’; Addition of ratio 6: 1 = 7, Multiple of 35
(6/7) x 35 = 30 boys, (1/7) x 35 = 5 girls
The correct answer is A, B and E.
Q.7 www.limaglobal.com
A. 96
B. 116
C. 112
D. 212
E. 115
3m2 + n2 = 3 x 42 + 82
= 48 + 64
= 112
The answer is ‘C’.
Q.8 www.limaglobal.com
If m : n = 3:5, and -2 < n <2
Quantity A Quantity B
m+ 4n 3m+n
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;
Let us bring both the quantities to a common variable ‘n’
Now put different values for ‘n’ between -2 to 2
| Quantity A | Quantity B | Remarks | |
| 1. n =1 | (23/5) x 1 = 4.6 | (14/5)x 1 = 2.8 | Quantity A is greater |
| 2. n = -1 | (23/5) x -1 = -4.6 | (14/5) x -1 = -2.8 | Quantity B is greater |
| 3. n = 0 | (23/5) x 0 = 0 | (14/5) x 0 = 0 | Both ‘A’ & ‘B’ same |
| 4. n =-2 | (23/5) x -2 = -9.2 | (14/5) x -2 = -5.6 | Quantity B is greater |
| 5. n = 2 | (23/5) x 2 = 9.2 | (14/5) x 2 = 5.6 | Quantity A is greater |
By reviewing the remarks column, we cannot arrive at a conclusion about which quantity is greater.
Hence, the answer is ‘D’.
Q.9 www.limaglobal.com
Which even number must be added to the ratio 5: 6, to make it equal to 9: 10?
A. 2
B. 4
C. 12
D. 8
E. 16
Solution:
Let us take the number to be added = m
(5+m): (6 + m) = 9: 10
(5+ m)/ (6 + m) = 9 /10
10 x (5 + m) = 9 x (6 + m)
50 + 10m = 54 + 9m
Transpose ‘9m’ to Right & 50 to Left
10m – 9m = 54 – 50
m = 4
The answer is ‘B’.
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Lima Global Institute of Virtual Learning
Q.10 www.limaglobal.com
There is 220-ounce mango juice in a glass, it has been shared by Albert, Maria and Alia such that Alia got one-sixth of Maria and remaining juice is divided between Albert and Maria in a ratio of 2:3. Find, how much ounces does Alia get?
A. 120
B. 50
C. 150
D. 60
E. 20
Solution:
Let us take that there is ‘m’ ounce of mango juice in a glass.
Sharing between Albert and Maria be 2m and 3m.
Alia’s share = 1/6 of Maria = (1/6) x 3m = (½) m
2 m + 3m + (1/2)m = 220
(4m + 6m + m)/2 = 220
11m = 220 x 2 = 440
m = 440/11
m = 40
Albert’s share = 2m = 2 x 40= 80 ounce.
Maria’s share = 3m = 3 x 40 = 120 ounce.
Alia’s share = (1/2) x m = ½ x 40 = 20 ounce.