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8th Grade > Mathematics

DIRECT AND INVERSE PROPORTIONS MCQs

Total Questions : 58 | Page 4 of 6 pages
Question 31.


If an SUV can transport 7 people, car can transport 5, jeep can transport 8 and auto can transport 2 people, which of the following combination can be used to exactly transport 25 people?


  1.     Two rounds of jeep, one round of SUV and one round of auto.
  2.     2 rounds of SUV, 2 rounds of car
  3.     One round of SUV and jeep each, two rounds of car
  4.     Three rounds of car, two rounds of SUV and on round of jeep
 Discuss Question
Answer: Option A. -> Two rounds of jeep, one round of SUV and one round of auto.
:
A and C

Let the number of rounds done by SUV be x, car be y, jeep be z and auto be p.
Thus the number of passengers transported will be 7x+5y+8z+2p ....   (1)
Checking options respectively:
1x=1,z=2,p=1
       Substituting these in (1)
       7+8 × 2+2=25.
       So option A is correct.
2x=2,y=2
       Substituting these in (1)
       7×2+85×2=24
       So option B is incorrect.
3x=1,y=2,z=1
       Substituting these in (1)
       7+5×2+8=25.
       So option C is correct.
4 Similarly substituting the values of option D. We will find number of people transported=26
 


Question 32.


10 men can reap a field in 20 days. 10 men reaped the field for 10 days and after 10 days 10 more men join them. When will the work be finished?


  1.     15 days
  2.     25 days
  3.     30 days
  4.     12 days
 Discuss Question
Answer: Option A. -> 15 days
:
A

Total number of work days required =10 x 20 = 200
Since 10 men worked for 10 days, 10 x 10 = 100 days work is already done.
So, 200 - 100 = 100 days of work is left. 
Once, 10 more men joined, total number of workers=20
So, number of days required more =10020=5
Thus, total number of days = 10 + 5 = 15.


Question 33.


An army camp of 250 men has provision for 350 days. After 25 days, 50 men died due to epidemic. The food will last for 


___ days.
 Discuss Question
Answer: Option A. -> 15 days
:

Remaining number of men = 250-50 =200 men
             Remaining number of days = (350-25) days = 325 days.
            250 men had provisions for 325 days
           1 man had provisions for (250 × 325) days  
          200 men had provisions for (250×325)200 days  

                                                                                       
                                          = 406.25days =406 days
        hence, the remaining food will last for 406 days.

 


Question 34.


Ipsa bought a car which covers 363 km in 24.2 litres of petrol. What will be the distance covered using 7 litres of petrol?


  1.     213 km
  2.     105 km
  3.     67 km
  4.     86 km
 Discuss Question
Answer: Option B. -> 105 km
:
B

Let the required distance be y.


Distance (in km)363yAmount of petrol(in l)24.27


The distance travelled and the amount of petrol consumed are directly proportional
AB= Constant
A1B1A2B2
Ipsa Bought A Car Which Covers 363 Km In 24.2 Litres Of Petr...


24.23637y
24.2×y=363×7


y=7×36324.2=105 km


Question 35.


I decided to purchase an anniversary gift for my parents. I selected gifts, 3 of which costs Rs.550. If I want to spend Rs.1100, I could purchase 6 gifts.


  1.     True
  2.     False
  3.     67 km
  4.     86 km
 Discuss Question
Answer: Option A. -> True
:
A

Number of gifts3yPrice (In Rupees)5501100
3550=y1100y=3×1100550=6 gifts


Question 36.


Shane has to fill a water tank in 3 hours 40 minutes and he used 7 pipes for that. How many pipes should he use to fill the tank in 1 hour 21 minutes?


  1.     21 pipes
  2.     19 pipes
  3.     7 pipes
  4.     30 pipes
 Discuss Question
Answer: Option B. -> 19 pipes
:
B

Let the number of pipes be y.


Number of pipes7yTime (in minutes)22081


Shane Has To Fill A Water Tank in 3 Hours 40 Minutes And He...The number of pipes and the time are inversely proportional.
AB = constant
A1×B1A2×B2
7y = 81220


y=7×22081=19.0119


Shane has to use 19 pipes to fill the tank in 1 hour 21 minutes.


Question 37.


4 oxen or 12 cows can graze a field in 32 days. How long would 7 oxen and 3 cows take to graze the same field?


  1.     12 days
  2.     17 days
  3.     32 days
  4.     16 days
 Discuss Question
Answer: Option D. -> 16 days
:
D

4 oxen = 12 cows
1 ox = 124 cows
 7 oxen124×7 cows=21 cows
  (7 oxen + 3 cows) (21 cows + 3 cows) = 24 cows
Now, 12 cows can graze the field in 32 days.
So, 1 cow can graze the field in (32×12) days.
[less cows, more days]
24 cows can graze the field in 32×1224=16 days
[more cows, less days]   
Hence, 9 oxen and 3 cows can graze the field in 16 days
.


Question 38.


A bottle filling machine can fill 238 bottles in 2hrs. In 7hrs, it can fill 


___ bottles.
 Discuss Question
Answer: Option D. -> 16 days
:

Number of bottles238yTime (In hours)27
The time taken and the number of bottles filled are directly proportional.
AB= Constant
A1B1A2B2
2238=7y
y=7×2382
y=833  bottles


Question 39.


39 men can build a bridge in 12 days, working 5 hours a day. In how many days will 30 men, working 6 hours a day, complete the work?


  1.     10
  2.     13
  3.     14
  4.     15
 Discuss Question
Answer: Option B. -> 13
:
B

Let the required number of days with 30 men working for 6 hours be x.
Number of men3930Number of hours56Number of days12x
Number of men, number of hours and number of days are inversely proportional and work done is constant in both the cases, hence
39×12×5=30× x ×6x=39×12×530×6x=13 days


Question 40.


A ball falls vertically after being dropped. The ball falls a distance d metres in a time of t seconds. d is directly proportional to the square of t.
The ball falls 20 metres in a time of 2 seconds.
The time (in seconds) that the ball takes to fall 605 m is


  1.     10
  2.     11
  3.     12
  4.     13
 Discuss Question
Answer: Option B. -> 11
:
B

Given distance s is directly proportional to square of time t.
That is:
 s=k.t220=4kk=5So,s=5t2605=5t2


t = 11 seconds


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