Unit-3:Commercial mathematics
(a) Percentage
(b) Profit and loss, discount, time and distance
(c) simple interest and compound interest
(d) Ratio and proportion
(e) Unitary methods and applications
Q1.
If a:b = 4:3, and a:c = 5:6 . find b:c.
(a)5/8 (b)4/3 (c)2/3 (d)6/5
Solution.
b/c = (b/a) x (a/c)
= 3/4 x 5/6
b/c = 5/8
Solution
Q2.
If 6A = 4B = 9C then find A:B:C ?
Solution.
Let 6A = 4B = 9C = x
A:B:C = x/6 : x/4 : x/9 = 1/6 : 1/4 : 1/9
A:B:C = 36/6 : 36/4 : 36/9 = 6 : 9 : 4
A:B:C = 6:9:4
Solution
Q3.
Find the third proportional to 8 and 12 .
Solution.
Let the third proportional to 8 and 12 be x.
Then , 8 : 12 :: 12 : x
8x = 144
x = 144/8
= 18
(Product of extremes =
Product of means)
Solution
Q4.
In an examination , a candidates A scores 20% and fails by 40 marks while candidates B scores 30% and gets 10 marks more than the minimum
pass marks . find the maximum marks.
Solution.
Let x is maximum marks
pass marks for A = 20% of x + 40
pass marks for B = 30% of x - 10
10% of x = 50
x = 500
Solution
Q5.
If 12 bananas are bought for Rs.11 and 11 bananas are sold for Rs.12. find gain or loss percent .
Solution.
C.P of 12 bananas = Rs.11
C.P of 1 banana = 11/12
S.P of 11 bananas = Rs.12
S.P of 1 bananas = 12/11
S.P > C.P
gain = 12/11 - 11/12
= (144 - 121/132) = 23/132
gain % = (23/132) x (12/11) x 100
= 2300/121
Solution
Q6.
In how many years a sum of money will be double if rate of interest is 9% .
Solution.
S.I = Prt/100
x = x9t/100
t=100/9
(In the case of double principle is equal to interest)
Solution
Q7.
If S.I is (1/16)th of the principal and the number of years is equal to rate percent. find the rate percent.
Solution.
Let the sum be Rs. P,
then SI = prt/100
p/16 = P x (x)2/100
x2 = 100/16
x = 10/4
= 2.5 yrs.
Solution
Q8.
In the case of compound interest amount of 3rd year will be the principal of 4th year.
Solution.
Yes
(amount = principal + interest)
Solution
Q9.
If x and y can complete a work in 25 days. If x is five times as good a workman as y . In how many days x alone finish the work ?
Solution.
x is five times as good work man as B
x's one day work = y's five day work
y's one day work = x's 1/5 day's work.
Given (x+y)'s 1 day work = 1/25
x's 1 day work + x's 1/5 days work = 1/25
x's 6/5 days work = 1/25
x's 1 day work = 1/30
So,x alone finish the work in 30 days .
Solution
Q10.
If a boat can travel at 16km/hr downstream and 14km/hr upstream . What is the speed of boat in still water .
Solution.
Let speed of boat in still water is x km/hr and the speed of currant is ykm/hr.
speed of boat in still water = 1/2 (x+y)
= 1/2(16 + 14)
= 15km/hr
Solution
