Class VIII
Answer Key
Subject: Mathematics
Chapter: Direct and inverse proportions, Introduction to graph
1. 5 men needed 40 days to complete the work. Since 4 days work is done, the remaining work
would have needed 35 men, 36 days to complete. Now there are 35-7=28 men.
Let number of days needed be x
Number of men
35
28
This is the case of inverse variation.
Number of days
36
x
So, 35 X 36 = 28 X x
x= 45
The remaining work will be completed in 45 days.
2. Now there are 16 +4 =20 people, so the food will last for less number of days.
Let number of days be x. This is the case of inverse variation.
So, 16 X 20 = 20 X x
Number of people
16
20
x= 16
Number of days
20
x
The food will last for 16 days.
3. Let x men will do the given piece of work in 14
Number of men
56
x
days. More the number of men, less will be the
number of days to finish the work. So it is a case
Number of days
42
14
of inverse variation
14 X x= 56 X 42
x= 168
Hence, 168 men will finish the given piece of work in 14 days.
4. Let the number of men required be x.
Number of men
11 x
Since length of trench dug and number
3
Length
of
trench
(in
meters)
27
of persons employed are in direct variation
6
4
11
𝑥
so, 3 =
6
4
27
x= 44
Hence the required number of persons= 44
5. The remaining food would last (45-10 =)3 5days for 150 men .But 25 men have left.
Number of remaining men= 150- 25= 125
Number of persons
For 150 men, food lasts 35 days. Suppose
Number of days
for 125 men, food lasts x days. Less men,
more days, so it is a case of inverse variation.
150 125
35
x
∴150 X 35 = 125 X x
x = 42
Number of cycles
52 x
Hence the food will last 42 days.
Cost of a cycle (in Rs.) 525 546
6. Let the number of bicycles he is able to buy= x
More the cost of cycle, less the number of cycle would he be able to buy and vice versa.
Therefore, it is a case of inverse variation.
52 X 525= x X 546
x= 50
Hence, the number cycles he would be able to buy = 50
7.
(i)
40
35
30
25
20
15
10
5
0
Sun
Mon
Tue
Wed Thru
Fri
Sat
(ii) Thursday was the coldest day
(iii) On Friday, the temperature was 25°𝐶
8. (i) 350 Km is distance travelled in 7 hours
(ii) 11 hours
(iii)Average speed travelled by a car = 50 Km/hr
9. (i) b
(ii)X axis
(iv) a) IV Quadrant
b) III Quadrant
d)I Quadrant
e) III Quadrant
10. a) 30 runs
b) 65 runs
d) 10 runs in match VI
e) 5 matches
g) match II
h) match VIII
11. Find the daily rate per hen.
Hens X Days X Daily rate) = Eggs
1
1
(iii) straight
c) II Quadrant
c)100 runs in match IV
f) match VII
1
12 𝑋 1 2 X (Daily rate)= 12
(Daily rate)=
1
2
1
1
2
1
2
(1 1 )
=
1
1
2
1
2
=3
So, 1 hen in 1 day will lay 2/3 of an egg.
a) Archimedes
b) Indians
c)Akbar