EXAMPLE PROBLEMS:
13. Difference of two numbers is 1660.If 7.5 % of one number is 12.5% of the other number. Find two numbers?
SOLUTION:
Let the two numbers be x and y.
7.5% of x=12.5% of y
So 75x=125 y
3x=5y
x=5/3y.
Now x-y=1660
5/3y-y=1660
2/3y=1660
y=2490
So x= 2490+1660
=4150.
So the numbers are 4150 , 1660.
14. In expressing a length 81.472 KM as nearly as possible with 3 significant digits ,Find the % error?
SOLUTION:
Error= 81.5-81.472=0.028
So the required percentage = 0.028/81.472*100%
= 0.034%
15. In an election between two persons ,75% of the voters cast their votes out of which 2% are invalid. A got 9261 which 75% of the total valid votes. Find total number of votes?
SOLUTION:
Let x be the total votes.
valid votes are 98% of 75% of x.
So 75%(98%(75% of x))) = 9261
==> 75/100 *98 /100 * 75 100 *x = 9261
x= 1029 * 4 *100 *4 / 9
= 16800
So total no of votes = 16800
16 . A's maths test had 75 problems i.e 10 arithmetic, 30 algebra and 35
geometry problems. Although he answered 70% of arithmetic , 40%
of algebra and 60 % of geometry problems correctly he didn't pass the
test because he got less than 60% of the problems right. How many
more questions he would have needed to answer correctly to get a
60% passing grade.
SOLUTION:
70% of 10 =70/100 * 10
=7
40% of 30 = 40 / 100 * 30
= 12
60 % of 35 = 60 / 100 *35
= 21
So correctly attempted questions = 7 + 12 + 21
=40.
Questions to be answered correctly for 60% grade
=60% of 75
= 60/100 *75
=45.
So required questions=45-40 = 5
17 . If 50% of (x – y) = 30% of (x + y) then what percent of x is y ?
SOLUTION:
50/100(x-y) =30/100(x+y)
½ (x-y)= 3/10(x+y)
5x-5y=3x+3y
x=4y
So Required percentage =y/x*100 %
=y/4y *100 %
= 25%.
18 . If the price of tea is increased by 20% ,find how much percent must a
householder reduce her consumption of tea so as not to increase the
expenditure?
SOLUTION:
Reduction in consumption= R/(100+R) *100%
=20/120 *100
= 16 2/3
