Unit-3:
(a) Ratio and proportion
(b) Percentage
(c) Partnership
(d) Average
(e) Problem based on ages
Q1.
Which statement is correct .
(a)Inverse ratio of 2:5 is 1/2 : 1/5 .
(b) Duplicate ratio of 2:3 is 4:9 .
(c) Inverse ratio is also called as reciprocal ratio.
(d) Sub triplicate ratio of 4:5 is (4)3:(5)3
Solution.
(d) Sub triplicate ratio of 4:5 is (4)3:(5)3
Solution
Q2.
If four quantities are there in proportion, the product of extremes is equal to the product of the means .
(a) True (b) False (c) Can't
Solution.
(a) True
Solution
Q3.
In 60 litres mixture of milk and water the ratio of milk and water is 7:3. Find the quantity of water to be added in the mixture in order
to make this ratio 3:7 .
(a) 20 litre (b) 80 litre (c) 40 litre (d) 10 litre
Solution.
= 42/18
42/(18 + x) = 3/7
294 = 54 + 3x
240 = 3x
x = 80
Solution
Q4.
If the sides of rectangle are increased by 20% , what is the percentage increase in its area ?
(a) 9% (b) 18% (c) 44% (d) 36%
Solution.
= (2x + x2/100)% = 2 x 20 + 400/100 = 44%
Solution
Q5.
Two numbers are respectively 10% and 25% less than a third number, what percent is the first of the second ?
(a) 75% (b) 120% (c) 100% (d) 80%
Solution.
[(100 - x)/(100 - y) x 100]%
(90/75) x 100 = (90/3) x 4
30 x 4 = 120%
Solution
Q6.
A,B and C invested capitals in the ratio 2:4:5, the timing of their investment being in the ratio 3:2:6 . Find their profit ratio .
(a) 3:4:15 (b) 2:1:1 (c) 4:6:3 (d) 7:8:9
Solution.
= 6:8:30
= 3:4:15
Solution
Q7.
Find the average of cube of first 12 natural numbers .
(a) 1106 (b) 507 (c) 606 (d) 908
Solution.
= [n(n + 1)2/4]
= [12(13)2/4]
= 3(169)
= 507
Solution
Q8.
Average of 3 numbers are 46, and the average of first two numbers are 25, find the value of third number.
(a) 48 (b) 52 (c) 60 (d) 88
Solution.
(d) 88
Solution
Q9.
The age of the father 3 years ago was 7 times the age of his son. At present the father's age is five times that of his son. find the age
of son ?
(a) 9 (b) 6 (c) 10 (d) 18
Solution.
let present age of son and father is x 5x respectively .
7(x - 3) = 5x - 3
7x - 21 = 5x - 3
2x = 18
x = 9
Solution
Q10.
One years ,ago the ratio between a's and b's age was 4:3 , one year hence the ratio of their age will 5:4 . What is the present age of A and
B .
(a) 9,7 (b) 9,8 (c) 9,6 (d) 8,9
Solution.
(a) 9,7
Let present age of A and B is x and y respectively .
(x - 1)/(y - 1) = 4/3 -----------1
(x + 1)/(y + 1) = 5/4 -------------2
Solution
