8th Grade > Mathematics
DIRECT AND INVERSE PROPORTIONS MCQs
:
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:
1→x=1,z=2,p=1
Substituting these in (1)
7+8 × 2+2=25.
So option A is correct.
2→x=2,y=2
Substituting these in (1)
7×2+85×2=24
So option B is incorrect.
3→x=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
:
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.
:
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.
:
A
Number of gifts3yPrice (In Rupees)5501100
3550=y1100⇒y=3×1100550=6 gifts
:
D
4 oxen = 12 cows
⇒ 1 ox = 124 cows
⇒ 7 oxen≡124×7 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.
:
Number of bottles238yTime (In hours)27
The time taken and the number of bottles filled are directly proportional.
AB= Constant
A1B1 = A2B2
2238=7y
⇒y=7×2382
⇒y=833 bottles
:
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
:
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