1.
The number of candidates writing three different entrance exams is in the ratio 4:5:6. There is a proposal to increase these numbers of candidates by 40%, 60%, and 85%, respectively. What will be the ratio of increased numbers?
Answer: Option 'B'
Given ratio of number of candidates is 4:5:6
Let the number of candidates for 3 exams be 4k, 5k, and 6k, respectively.
After increasingthenumberof candidates by 40%, 60% and 85%, respectively.
=> Number of candidates become (140% of 4k),(160% of 5k),(185% of 6k)
=> (140x4k) /100, (160x5k)/100 and (185x6k) /100
= 56k/10, 80k/10, and 111k/10
Now, the required new ratio is: 56k/10: 80k/10 : 111k/10
= 56 : 80 : 111
2.
If a dozen mirrors are fallen down. The ratio between broken and unbroken mirrors is:
Answer: Option 'C'
Dozen means = 12
12/(2+3) = 12/5 ==> wrong
12/(3+4) = 12/7 ==> wrong
12/(5+7) = 12/12 = 1 ==> Right (Answer = 5:7)
3.
Two numbers are in the ratio 11:12, if 14 is added to each they are in the ratio 69:74. Find the two numbers.
Answer: Option 'A'
Numbers are in the ratio 11 : 12
Two numbers are 11k and 12k
Adding 14 to both the numbers, 11k+14 and 12k+14
Given that 11k+14 : 12k+14 = 69 : 74 => 74(11k+14) = 69(12k+14) => (814-828)k = 14 x (-5) => k = 5
First Number, 11 x k = 55 Second Number 12 x k = 60
Numbers are 55 and 60
4.
If Rs.1440/- are divided among A,B and C so that A receives 1/3rd as much as B and B receives 1/4th as much as C. The amount B received is:
Answer: Option 'B'
A:B:C = 1:3:12
Total parts = 16
B's share is = 3 parts
16 -----> 1440
1 -----> 90
3 -----> 270 (B's share is 270)
5.
The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
Answer: Option 'D'
3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ----> 4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)
6.
The ratio of number of boys and girls in a school of 720 students is 7:5. How many more girls should be admitted to make the ratio 1:1?
Answer: Option 'B'
Given, boys : girls = 7 : 5
Let, the total number of boys = 7x
and total number of girls= 5x
Given, total students = 720
=> 7x + 5x = 720
=> 12x = 720
=> x = 60
so, total number of boys = 7x = 7 * 60 = 420
and total number of girls= 5x = 5 * 60 = 300
Let "y" be the number of girls added to make the ratio 1 : 1
=> 420 / (300 + y) = 1/1
=> 420 = (300 + y)
=> y = 420 - 300
=> y = 120
So, 120 more girls should be admitted to make the ratio 1:1
7.
The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
Answer: Option 'C'
Let the three numbers be A, B, C.
Then, A : B = 2 : 3 and
B : C = 5 : 8
Now, A : B = 2 : 3
=> A : B = (2 × 5) : (3 × 5) = 10 : 15
Now, B : C = 5 : 8
=> B : C = (5 × 3) : (8 × 3) = 15 : 24
Thus, A : B : C = 10 : 15 : 24
=> A = 10x, B = 15x, C = 24x
Given, A + B + C = 98
=> 10x + 15x + 24x = 98
=> 49x = 98
=> x = 2
Thus, Second number, B = 15x = 15 × 2 = 30
8.
Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?
Answer: Option 'D'
= 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 × 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 × 6 = 24)
9.
Two numbers are in the ratio 2:3. If eight is added to both the numbers, the ratio becomes 3:4. The numbers are
Answer: Option 'B'
Numbers be m and n, m/n = 2/3 (m+8)/(n+8) = ? => m=16 and n= 24
10.
If A:B = 3:2 B:C= 4:3 then A:B:C=?
Answer: Option 'A'
(6:4:3)
11.
If x:y=5:3 then (8x-5y) : (8x+5y)=?
Answer: Option 'C'
x/y = 5/3 (Given)
(8x − 5y)/(8x + 5y)
8(x/y) − 5/8(x/y)+5
( on dividing Nr and Dr by y)
(8(5/3) − 5)/(8(5/3) + 5)
(40/3 − 5/1)/(40/3 + 5/1)
[(40 − 15)/3]/[(40 + 15)/3]
25/55 = 5/11
(8x-5y):(8x+5y) = 5:11
12.
Find the third proportional to 9 and 12?
Answer: Option 'C'
Formula = Third proportional = (b × b)/a
A = 9 and B = 12
(12 × 12)/ 9 = 144/9 = 16
13.
Ratio between two numbers is 3 : 2 and their difference is 225, then the smaller number is:
Answer: Option 'B'
Given, the ratio of two numbers = 3 : 2
Let the two numbers be 3x and 2x
Given, their difference = 225
=> 3x - 2x = 225
=> x = 225
Smaller number = 2x = 2 × 225 = 450
14.
If Rs.800/- Rupees are divided among a,b and c in such a way that A’s share 4 times more than B, B’s share is 3 times more than C. The C’s share is?
Answer: Option 'D'
A:B:C = 12:3:1
Total parts = 16
C's share is = 1 parts
16 -----> Rs.800/-
1 -----> Rs.50/- (Answer = Rs.50/-)
15.
A mixture contains milk and water in the ratio 5:2. On adding 10 liters of water, the ratio of milk to water becomes 5:3. The quantity of milk in the original mixture is?
Answer: Option 'A'
milk:water = 5:2
5x : 2x + 10 = 5 : 3
3[5x] = 5[2x + 10]
15x = 10x + 50
15x - 10x = 50
x = 10
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7
7x = 70
Short cut method:
milk:water = 5 :2
after adding 10 liters of water
milk:water = 5 :3
milk is same but water increse 10liters then the water ratio is increse 1 parts
1 part ---> 10 liters
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7
7 parts ---> 70 liters (Answer is = 70)
Short cut method - 2 : for Only milk problems
milk : water
5 : 2
5 : 3
milk ratio same but water ratio 1 part incress per 10 liters
1 part of ratio ---> 10 liters
7 part of ratio ---> 70 liters