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1. The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and that of second to the third is 5 : 8 then the second number is?
A. 20
B. 30
C. 38
D. 48
E. 52
Correct option is : B
Solution:
a:b= 2:3
b:c = 5:8
a:b:c =10 : 15 : 24
a+b+c = 98
49k = 98
k = 2
=> b = 15*2 = 30
2. The total number of students in a school is 31700. If the ratio of boys to the girls in the school is 743:842 respectively, what is the total number of girls in the school?
A. 14860
B. 16480
C. 15340
D. Cannot be determined
E. None of these
Correct option is : B
Solution:
Boys : Girls = 743 : 842
Total number of students = 31700
Number of girls = [842 / (743 +842)] × 31700
= (842 /1585) × 31700
= 16840
3. A sum of Rs. 221 is divided among X, Y and Z such that X gets Rs. 52 more than Y. Y gets Rs. 26 more than Z. The ratio of the shares of X , Y and Z respectively is
A. 9:5:3
B. 9:3:5
C. 5:9:3
D. 10:6:5
E. None of these
Correct option is: A
Solution:
221 is divided among X, Y and Z. Y gets Rs.(Z + 26)
X gets Rs. (Z + 26 + 52) = Rs. (Z + 78)
According to the question
Z + 78 + Z +26 + Z = 221
=> 3Z + 104 = 221
=> Z = 117/3
=> Z = 39
X = 39 + 78 = 117
Y = 39 + 26 = 65
Z = 39
117 : 65 : 39 = 9 : 5 : 3
4. The cost of making an article is divided between materials, labour and overheads in the ratio of 3:4:1. If the material cost Rs. 234, then the labour cost?
A. Rs. 176
B. Rs 312
C. Rs. 78
D. Rs. 390
E. None of these
Correct option is : B
Solution:
Cost of making is divided among material :labour : overheads = 3: 4: 1
Total material cosy = Rs. 234
3x = 234
=> x = 78
=>Labor cost = 4 X 78 = Rs. 312
5. In a school the number of boys and that of the girls are in the respective ratio of 2:3. If the number of boys is increased by 20% and that of girls is increased by 10%, what will be the new ratio of number of boys to that of the girls?
A. 14:5
B. 5:8
C. 13:4
D. Data inadequate
E. 8:11
Correct option is : E
Solution:
Ratio of boys and girls in the school = 2:3
New, increased value = 2 * 120/100: 3 * 110/100= 240 : 330
=>24 : 33 = 8:11
6. The ratio between two numbers is 2:3. If each numbers is increased by 4, the ratio between then become 5:7, the difference between numbers.
A. 8
B. 6
C. 4
D. 2
E. None of these
Correct option is : A
Solution:
Ratio between two numbers = 2:3
Let x is the common factor between the ratio (2x + 4)/(3x + 4) = 5/7
=> 14x + 28 = 15x + 20
=> x = 8
=> Required difference = (3x-2x) = 8
7. What number has to be added to each term of 4 : 7 to make the ratio 5 : 6?
A. 13
B. 12
C. 10
D. 11
E. None of these
Correct option is : D
Solution:
Let the number to be added be x As per statement,
(4 + x) / (7 + x) = 5/6
Cross multiplying, we get 24 + 6x = 35 + 5x
6x – 5x = 35 – 24
x = 11
8. In the 45 litres mixture of milk and water, the ratio of milk and water is 5 : 4. Find the quantity of water required to be added so that the resultant mixture will be in the ratio 4 : 5.
A. 7.75 litres
B. 11.25 litres
C. 9.25 litres
D. 12.50 litres
E. None of these
Correct option is : B
Solution:
The ratio of milk and water is 5 : 4,
The total quantity is 45 litres.
9’s=45
=>1’s=5
So Milk=25, Water=20
25/(20+x)=4/5 (Here x is the quantity of water to be added)
=>x=11.25 litres
9. Two natural numbers are in the ratio of 4 : 7 and their product is 112. Find both the numbers.
A. 4 and 7
B. 8 and 14
C. 12 and 21
D. 16 and 28
E. None of these
Correct option is : B
Solution:
Let, Natural numbers are 4x and 7x, then
4x * 7x = 112
28x2 = 112
x2 = 4
=> x = 2
=> Numbers are 8 and 14
10. The monthly income of A and B is in the ratio of 4 : 3 and their monthly expenditure is in the ratio of 3 : 2. If each of them saves Rs.6000 per month, the income of B is
A. 12000
B. 24000
C. 18000
D. 36000
E. None of these
Correct option is : C
Solution:
Let Monthly income of A = 4x
And, Monthly income of B = 3x
Also, Monthly expenditure of A = 3y
And, Monthly expenditure of B = 2y
Since the both save Rs.6000 each per month,
Therefore, 4x – 3y = 6000
Also, 3x – 2y = 6000
By solving the equations, we get,
x = 6000 and y = 6000
=> Monthly income of B = 3x = 3 * 6000 = Rs.18000