In a competitive exam, the number of passed students was four times the number of failed students. If there had been 35 fewer appeared students and 9 more had failed, the ratio of passed and failed students would have been 2 : 1, then the total number of students appeared for the exam ?

1. 170
2. 165
3. 180
4. 155 

Solution: 
Let the number of failed students be x
Number of passed students = 4x
So total number of students was 5x
From the given data
If total number of students be 5x – 35
(5x-35)/x+9=3/1
x = 31
Total number = 31×5 = 155 

Question :3 A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B, then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket?

1. 16.5 l
2. 18 l
3. 14.5 l
4. 15 l 

Solution:

Let bucket contains 5x and 3x of liquids A and B respectively.
When 16 litres of mixture is replaced, A and B has a mixture is
[5x – (5/8)*16] = (5x – 10)
[3x – (3/8)*16] = (3x – 6)
Ratio (5x – 10)/(3x – 6+16) = 3/5
(5x – 10)/(3x +10) = 3/5
X=5.
So, quantity of liquid B initially,
= 3*5 = 15 litres.

Hence, option 4 is the correct answer.

Question:4  In a Temple every devotee offers fruits to the orphans. Thus every orphan receives Mango, apple and grapes in the ratio of 2 : 5 : 7 in terms of dozen. But the weight of a grape is 35 gm and weight of a mango and an apple are in the ratio of 5 : 6, while the weight of an apple is 180 gm. Find the ratio of all the three fruits in terms of weight, that an orphan gets:

1. 55:140:32
2. 60:180:49 
3. 45:122:37
4. 44:153:48

 Solution:

Weight of Mango and Apple 5:6
Apple 6 180gm
Mango 5 150gm
Grape 35gm
Ratio 2:5:7
Required ratio of fruits by weight
=2*150 : 5*180 : 7*35
=60:180:49.

Hence, opiton 2 is the correct answer.

Question:5 The value of a diamond is directly proportional to the square of its weight. A diamond unfortunately breaks into three pieces with weights in the ratio of 3: 4: 5, thus a loss of Rs. 9.4 lakh is incurred. What is the actual value of diamond :

1. 15Lakh
2. 18Lakh
3. 16.5Lakh
4. 14.4Lakh 

Solution:

The ratio of broken part 3:4:5
Value of broken parts of diamond =3x² +4x²+5x²=50x²
Value of original diamond 12x²=144x²
Then loss= 144x²-50x²=94x²
94x²=9.4Lakh
x²=1/10 Lakh
Actual value= 144x²=144x 1/10
=14.4Lakh

Hence, option 4 is the correct answer.

Question:6   Rs 1440 were distributed among A ,B,C and D in such a way that C and D together gets half of what A and B together gets and C gets one third amount of B. Also D gets 5/3 times as much as C. what is the amount of A?

1. Rs560
2. Rs420 
3. Rs460
4. Rs545

Solution:

Given
C+D= (A+B)/2
B:C 3:1
C:D 3:5
B:C:D 9:3:5
(A+B)=2(C+D)
A+9x=2(3x+5x)
A=7x.
Total (7+9+3+5) 24 x=1440==>x=60
Then 7x=7*60==>420

Hence, option 2 is the correct answer.