1] The average age of students of a class is 15.8 years.The average age of boys in the class is 16.4 years and that of the girls is is 15.4 years.The ratio of the numbers of boys to the girls in the class is
a]2:3 b]3:2 c]3: 5 d] 2:5

let the ratio be a:b
total number of boys  = 16.4*a
total number of girls  = 15.4*b
total number of students in class = 16.4a + 15.4b
the average age of all students is 15.8
the average age of boys is 15.8 a
the average age of girls is 15.8b
16.4a + 15.4b = 15.8a + 15.8b
0.6 a = 0.4 b
a/b = 0.4/0.6 = 2/3

1]A man bought a number of clips at 3 for a rupee and an equal number at 2 for a rupee.At what price per dozen should he sell them to make a profit of 20%
a]12 b]6 c]10 d] 2

Lets assume a dozen of clips were brought at 3 for a rupee and another dozen of clips were brought at 2 for a rupee
total CP for 1 dozen in which the cost is 3 for a rupee= 12/3 =4
total CP for 1 dozen in which the cost is 2 for a rupee= 12/2 = 6

total cp for 2 dozens = 6+4 = 10
percentage profit = 20% on Rs. 10 = 20/100 * 10 = Rs.2
After percentage profit the SP of 2 dozen is
Profit = SP - CP
SP = Profit + CP
SP = 2+ 10 = 12
SP of 1 dozen = 12/2 = 6

1] Find the average of first nine multiples of 3
a]12 b]12.5 c]15 d]18.5

average = 3[1+2+3+4+5+6+7+8+9] / 9 = (3*45) /9 = 15

2] Find the average of first twenty multiples of 7
a]72 b]42.5 c]15.6 d]73.5

3] Find the average of first five multiples of 3
a]12 b]12.5 c]15 d]9

4] Find the average of first five multiples of 4
a]12 b]12.5 c]15 d]18.5

5] Find the average of first ten multiples of 3
a]12 b]16.5 c]15 d]18.5

1]A and B together can do a work in 8 days.If A alone can do it in 12 days,then in how many days can B alone do it?

time for [A + B]'s days 1 work = 1/8
time for A's days 1 work =  1/12
time for B's days 1 work = ?

Time of [A+B]'s 1 day work = Time of A's 1 day work + Time of B's 1 day work
1/8 = 1/12+ B
B = 1/8 - 1/12 = 1/24

B's 1 days work = 24 days

1]A rectangle had width 'a' and length 'b'.If the width is decreased by 20% and the length is incresed by 10%.Then what is the area of the new rectangle in percentage compared to ab?
a]12 b]22 c]32 d]42
Let original length be 'b' and 'a'
original area = ab
new length = [(100+10)/100]  * b= (110/100)* b
new breadth = [(100-20)/100] * a = (80/100)*a
new area = (110/100) * b * (80/100)* a = (88/100) *ab
change area = ab - (88/100) * ab = 12 ab/100
% change  or decrease = 12ab/100 * (1/ab) * 100 = 12

2]If the length of a rectangle is increased by 30% while its breadth is decreased by 20%.What is happens to its area?
a]10% decrease b]10% increase c]4% decrease d]4% increase

3]If the length of a rectangle is increased by 70% while its breadth is decreased by 20%.Then percentage decrease in area will be
a]30%  b]32% c]36% d]34%

4]If the length of a rectangle is increased by 10% while its breadth is decreased by 10%.The area of new rectangle is
a]neither increased or decreased b]1% increase c]1% decrease d]none

5]If the length of a rectangle is doubled while its breadth is halved.Then percentage change in area will be
a]50 b]75 c]no change d]none