Unit-3:
(a) Ratio and proportion
(b) Percentage
(c) Partnership
(d) Average
(e) Problem based on ages
Q1.
Find the third proportional to 10, 15
(a) 22.5 (b) 10 (c) 15 (d) 18.5
Solution.
10:15 = 15:x
10x = 225
x = 22.5
Solution
Q2.
If 9 men can do a piece of work in 60 days of 8 hours each, how many men will it take to do 5 times the amount work if they work for 30 days of 8 hours.
(a) 40 (b) 90 (c) 60 (d) 30
Solution.
W2 x M1 x D1 x H1 = W1 x M2 x D2 x H2
5 x 9 x 60 x 8 = 1 x M2 x 30 x 8
M2 = 90 men
Solution
Q3.
The students in three section are in the ratio 2:3:5 . If 40 students are increased in each section , the ratio changes to 4:5:7 .
what is the total strength before the increase.
(a) 90 (b) 150 (c) 100 (d) 200
Solution.
4x - 2x = 2x (that is same for all section)
2x = 40
x = 20
= 2x + 3x + 5x
= 10x
= 10 x 20
= 200
Solution
Q4.
In a fashion designing institute the number of seats increased by 25% and the fees is also increased by 10% . what will be the impact
on the total revenue collected.
(a) 48% (b) 36% (c) 37.5% (d) 40%
Solution.
= {a + b + ab/100}%
= 25 + 10 + (25 x 10)/100
= 37.5%
Solution
Q5.
A began a business with Rs. 900 and joined after wards by B with Rs.600 for how many months B was in business if at the end of the year profit
divided in the ratio of 2:1 ?
(a) 7 months (b) 9 months (c) 6 months (d) 8 months
Solution.
A's capital x A's time/B's capital x B's time
=
A's profit/B's profit
900 x 12/600 x (x)
=
2/1
900 x 12 = 1200x
900 = 100x
x = 9
Solution
Q6.
A and B joined a business with capitals as 1:1 at the end of 6 months, A withdrew . If they receive profits in the ratio 6:7 .
find how long B's
capital was used .
(a) 10 months (b) 9 months (c) 7 months (d) 6 months
Solution.
(c) 7 months
Solution
Q7.
Average of x is 10, find the average of y = 2x + 10 .
(a) 40 (b) 30 (c) 10 (d) 20
Solution.
(b) 30
Solution
Q8.
A student secured average N marks in the first time exams . In the 4th exam he secured (20 + N) marks , find the average of all
four exams .
(a) N + 5 (b) N (c) 4 (d) N + 6
Solution.
(a) N + 5
Solution
Q9.
The ratio of the ages of the father and the son at present is 6:1 . After 5 years the ratio will become 7:2, find the sum of ages(father & son)
(a) 50 (b) 35 (c) 40 (d) 45
Solution.
(b) 35
6x + 5/x + 5
=
7/2
12x + 10 = 7x + 35
5x = 25
x = 5
Solution
Q10.
The sum of present age of A, B and C is 90 year . Six years ago their ratio of age was 1:2:3 , find the present age of C .
(a) 18 (b) 36 (c) 40 (d) 42
Solution.
(d) 42
Six years ago their ages was x , 2x , 3x
So, x + 6 + 2x + 6 + 3x + 6 = 90
6x + 18 = 90
6x = 72
x = 12
Solution
