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Published on: 07/09/2019
Direct & Inverse Proportions
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Questions + Answers key
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1.
If a deposit of Rs 3000 earns an interest of Rs.600 in 3 years, then how much interest would a deposit of Rs. 36000 earn in 3 yr with the same rate of simple interest?
2.
In a camp, there is enough flour for 300 persons for 42 days. How long will the flour last, if 20 more persons join the camp?
3.
A car takes 2 hours to reach a destination by travelling at the speed of 60 km/h. How long will it take when the car travels at the speed of 80 km/h?
4.
Seema types 582 words during half an hour. How many words would she type in 10 min?
5.
A mixture of paint is prepared by mixing 1 part of red pigment with 8 parts of base. In the following table, find the parts of base that need to be added.
| Parts of red pigment | 1 | 4 | 7 | 12 | 20 |
| Parts of base | 8 | ... | ... | ... | ... |
if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?
6.
A girl 1.2 m tall casts a shadow 1.1 m at that height. When a building casts a shadow 6.6 m long. Determine the height of the building?
7.
A loaded truck travels 14 km in 25 min. If the speed remains the same, how far can it travel in 5h?
8.
If x and y are in inverse proportion, check whether (x + 1)and (y + 1) are also in inverse proportion
9.
If 45 students can consume a stock of food in 2 months, then find how many days the same stock of food will last for 27 students?
10.
If the area of a circle, whose radius is 5 cm is increased to four times, then find the changed radius?
11.
The AC two tier railway fare for 580 km of journey is Rs.3200. What would be the fare for a journey of 738 km?
12.
If Subhash bought 17 registers for Rs.340, then find the cost of 5 such registers
13.
If the weight of 9 sheets of thick paper is 30 g, how many sheets of the same paper would weigh \(1\frac{1}{4}kg?\)
375
250
925
300
14.
Both x and y are in direct proportion,then \(\frac{1}{x}\)and \(\frac{1}{y}\)are
in direct proportion
in inverse proportion
neither in direct nor in inverse proportion
sometimes in direct and sometimes in inverse proportion
15.
18 workers can do a work in 180 days. If two more workers join this work, the work will be completed in
140 days
150 days
158 days
162 days
16.
If two quantities p and q vary inversely with each other, then
\(\frac{p}{q}\)
p + q remains constant
p x q remains constant
p - q remains constant
17.
Both u and v vary directly with each other. When u is 10, v is 15, which of the following is not a possible pair of corresponding values of u and v?
15 and 20
2 and 3
25 and 37.5
16 and 24
18.
If on increasing a, b decreases in such a manner that______________remains____________and positive, then a and b are said to vary inversely with each other.
19.
When the speed remains constant, the distance travelled is______________ proportional to the time.
20.
If xy = 10, then x and y vary__________ with each other.
21.
x and y are said to vary directly with each other, if for some positive number k,...................=k
22.
Let x varies directly as y2, for y = 3, x = 2. If y = 5 then x is____________
23.
When the speed is kept fixed, time and distance vary directly with each other.
24.
If d varies directly as t2, then we can write dt2 = k, where k is some constant.
25.
If x varies inversely as y and when x = 6, y = 8, then for x = 8 the value of y is 10.
26.
If 5 persons can finish a job in 10 days, then 1 person will finish it in 2 days.
27.
The population of a country and the area of land per person are in direct proportion
1.
Rs.7200
2.
As number of persons increases, number of days will decreases for finishing the same amount of flour.
This is a case of inverse proportion.
Let number of persons = n
Number of days = d
\(n\propto \frac { 1 }{ d } \)
Here, n1 = 300, d1 = 42 days.
n2 = 300 + 20 = 320, d2 = ?
300 \(\times\) 42 = 320 \(\times\) d2
\({ d }_{ 2 }=\frac { 300\times 42 }{ 320 } =\frac { 315 }{ 8 } =39\frac { 3 }{ 8 } days\)
3.
Let car takes x h when the car travels at the speed of 80 km/h.
Then, we have the following table:
| Speed (in km) | 60 | 80 |
| Number of hours | 2 | x |
Obviously, if the speed of car increases, then the time taken to reach a destination will decreases.
Therefore, it is the case of inverse proportion.
\(60\times 2=80\times x\Rightarrow x=\frac { 60\times 2 }{ 80 } =\frac { 3 }{ 2 } =1\frac { 1 }{ 2 } \)
Hence, car would take \(1\frac { 1 }{ 2 } \) h or 1h 30 min, when the car travels at the speed of 80 km/h.
4.
194 words
5.
Let the number of parts of red pigment be x and the amount of base = y mL
Here, x1 = 1,y1 = 75 and y2 = 1800, x2 = ?
\(\Rightarrow \frac { 1 }{ 75 } =\frac { { x }_{ 2 } }{ 1800 } \Rightarrow { x }_{ 2 }\times 75=1\times 1800\)
\({ x }_{ 2 }=\frac { 1800 }{ 75 } =24\Rightarrow { x }_{ 2 }=24\)
Hence, 24 parts of red pigment should be mixed with 1800 mL of base.
6.
7.2
7.
Let distance covered and time taken by truck be x km and y h, respectively,
We know that,\(speed=\frac { Distance }{ Time } \)
\(⇒\) Distance = Speed \(\times\) Time
Hence, speed remains the same, so the distance covered would be directly proportional to time.
Here, x1 =14km and \({ y }_{ 1 }=25min=25\times \frac { 1 }{ 60 } h\left[ \because 1min=\frac { 1 }{ 60 } h \right] \)
\({ y }_{ 1 }=\frac { 25 }{ 60 } =\frac { 5 }{ 12 } hand{ y }_{ 2 }=5h\)
Now, by using relation \(\frac { { x }_{ 1 } }{ { y }_{ 1 } } =\frac { { x }_{ 2 } }{ { y }_{ 2 } } \)
\(\frac { 14 }{ \frac { 5 }{ 12 } } =\frac { { x }_{ 2 } }{ 5 } \Rightarrow { x }_{ 2 }\times \frac { 5 }{ 12 } =5\times 14\)
\({ x }_{ 2 }=\frac { 5\times 14\times 12 }{ 5 } =14\times 12=168km\)
Hence, loaded truck can travel upto 168 km in 5 h.
8.
We can check this with the help of the following example
For x = 2 and y= 3,
If x and y are in inverse proportion, then
xy = constant, xy = 2 \(\times\) 3 = 6
If we add 1in both x and y, then
x + 1 = 2 + 1 = 3 and y + 1 = 3 + 1 = 4
(x + 1)(y + 1) = 3\(\times\)4 =1 2 ≠ 6
Hence, if x and yare in inverse proportion, then (x + 1 ) and (y + 1 ) will not be in inverse proportion.
9.
100 days
10.
Change in radius = 10cm
11.
Rs.4071.72
12.
Rs.100
13.
(a)
375
14.
(a)
in direct proportion
15.
(d)
162 days
16.
(c)
p x q remains constant
17.
(a)
15 and 20
18.
( )
ab,constant
19.
( )
directly
20.
( )
inversely
21.
( )
\(\frac{x}{y}=k\)
22.
( )
\(x=5\frac{5}{9}\)
23.
(a)
24.
(b)
25.
(b)
26.
(b)
27.
(b)
8th Standard CBSE Syllabus & Materials
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CBSE 8th Standard CBSE Subjects
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