1 . 
If the length and the breadth of a rectangle is increased by 25% and 44% respectively, by what per cent does the area of that rectangle increase ?


Answer & Explanation
Answer : Option
D


Explanation : 

Let the initial length and breadth be 100m each, therefore, after increase it will be 125m and 144m respectively. Initial area = 100 x 100 = 10000 sq m After increase, the area will be 125 x 144 = 18000 sq m
∴ Percentage increase in area
= (18000  10000)/10000 x 100 = 80
ie increase = 80%
other approach
25 + 44 + 25x44/100 = 80%






2 . 
In a 150litre mixture of milk and water, the percentage of milk is 84%. How much water should be added so that the percentage of milk becomes 52.5% ?


Answer & Explanation
Answer : Option
C


Explanation : 

In 150 litre, milk is 84%
ie 150 x 84/100 = 126 litre
Let us add x litres of water Therefore, the quantity of mixture = 150 + x
∴ 52.5% of (150 + x) = 126 litres
150 + x = 126x100/52.5 = 240 litres
∴ x = 240  150 = 90 litres






3 . 
A man covers a certain distance on car. Had he driven 21 kmlr1 faster, he would have taken 7 hours less. If he had driven the car 13 kmlr1 slower, he would have taken 13 hours more. What is the distance ?


Answer & Explanation
Answer : Option
D


Explanation : 

Let the distance be x km and speed y kmh1
or, x/y = x/(y + 21) + 7
or, x/y  x/(y + 21) = 7
or, x (1/y  1/y + 21) = 7 ...... (I)
x/y = x/(y  12) =  13 ...........(II)
Dividing (I) hy (II), 1/y  1/(y + 21)
= 7/13 (1/y  1/y  13)
or, y + 21  y/y(y + 21)
= 7/13 (y  13  y/y(y  13))
or, 21/y(y + 21) = 7/y(y  13)
∴ 3/y + 21 = 1/y  13
or, 3y  39 = y + 21
or, 2y = 60 ∴ y = 30
x (1/y  1/y + 21) = 7
x (1/30  1/51) = 7
∴ 7x/510 = 7
∴ x = 510
∴ Distance = 510 km






4 . 
In a fraction, if the numerator is increased by 20% and the denominator is decreased by 40%, what will be the ratio of the first fraction to the second ?


Answer & Explanation
Answer : Option
A


Explanation : 

Let the original fraction be x/y.
Now x_{1} = x + x 20/100 = x + x/5 = 6x/5
y_{1} = y  y x 40/100 = y  2y/5 = 3y/5
∴ x_{1}/y_{1} = 6x/5 x 5/3y = 2x/y
∴ Reqd ratio = x/y / 2x/y = x/y x y/2x = 1/2






5 . 
Rajeev invested an amount of ?75000 to start a business. After 18 months his friend Suresh joined him with an amount of ?90000. At the end of 4 years they earned a profit of ?36281. What was the share of Suresh in the profit ?


Answer & Explanation
Answer : Option
A


Explanation : 

The ratio of Rajeev and Suresh's profit
= 75000 x 4 : 90000 x 2.5 = 4 : 3
∴ Suresh's share = 36281/7 x 3 = 15549






6 . 
Direction (Q. 610): Each of the questions below consists of a question and two statements (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question.
What is the sum of the ages of A, B and C ?
(I) The ratio of the age of A to that of B is 3 : 5
(II) The ratio of the age of B to that of C is 1 : 2.


Answer & Explanation
Answer : Option
D


Explanation : 

Data is not sufficient because we need exact age of any one of A, B or C to solve the question.






7 . 
What is the value of 70% off (x + y) ?
(I) x  y = 20
(II) x^{2}  y^{2} = 2800


Answer & Explanation
Answer : Option
D


Explanation : 

From (I), x  y = 20 ......(I)
From (II), x^{2}  y^{2} = 2800
∴ (x + y) x (x  y) = 2800
From eqn (I), x  y = 20
∴ x + y = 2800/20 = 140
∴ 70% of (x + y) = 70/100 x 140 = 98






8 . 
What is a twodigit number if the ratio of the digit at ten's place to the digit at unit's place is 4 : 3 ?
(I) The sum of the digits of a twodigit number is 14.
(II) The digit at unit place is 75% of the digit at ten's place.


Answer & Explanation
Answer : Option
A


Explanation : 

Let the number be 10x + y
∴ 3x = 4y ......(1)
From (I), x + y = 14 .....(2)
Solving equations (1) and (2), x = 8, y = 6
∴ Number = 86
From (II) y = 75/100 x x
∴ 3x = 4y. Which is the same as eqn (1)






9 . 
What is the average age of boys in a class if the ratio of the number of boys to that of girls is 3 : 2 and the average age of the boys and girls of the class is 13 years ?
(I) The average age of the girls in the class is 11.5 years.
(ll) The difference between the number of boys and girls is 10.


Answer & Explanation
Answer : Option
D


Explanation : 

Let the number of boys and girls be
3x and 2x respectively
From (II) 3x  2x = 10
∴ x = 10
∴ boys = 3x = 30 and girls = 20
From (I), Total age of 20 girls = 11.5 x 20 = 230 years.
Total age of all boys and girls = 50 x 13 = 650 years
∴ Total age of boys = 650  230 = 420 years
∴ Average age of boys = 420/30 = 14 years






10 . 
What is the length of a train
(l) It takes 7.5 seconds to cross a pole.
(ll) It takes 17 seconds to cross a 190metrelong bridge.


Answer & Explanation
Answer : Option
D


Explanation : 

Let the length of the train be x metres and the speed be V ms1
From (I), x/v = 15/2 ∴ 2x = 15v ...... (1)
From (II), x + 190/v = 17
∴ x + 190 = 17v ......(2)






