Chain Rules - Online Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to Chain Rules. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.
Q 1 - A worker makes a toy every 2/3 hour. If he works for 15/2 hours, then how many toys will he makes?
A - 45/4
B - 47/4
C - 53/4
D - 55/4
Let the required number of toys be x.
More time , more toys made   (Direct)
2/3 : 15/2 :: 1:x ⇒ 2/3 * x = 15/2 *1 ⇒ x= (15/2 *3/2 ) = 45 /4 = 45/4.
Required number  of toys = 45/4.
Q 2 - The Qutab minar casts a shadow 150m long at the same  time when the vikes minar casts a shadow 120m long on the ground . If the height of the Vikes minar is 80m, what is the height  of the Qutab Minar?
A - 100m
B - 120m
C - 150m
D - 180m
Let the height of  the Qutab Minar be x metres.
Longer is the shadow , longer is the object    (Direct)
120 : 150 :: 80 : x ⇒ 120 * x = (150 *80)⇒ x= (150 *80)/120=100m.
Height of Qutab Miinar = 100m.
Q 3 - 10 pipes of the same diameter can fill a tank in 24 minutes. If 2 pipes go out of order, how long will the remaining pipes takes to fill the tank?
A - 40 min
B - 45 min
C - 30 min
D - 96/5 min
Let the required time be x minutes.
Less pipes, more time     (Indirect)
8: 10 ::24 : x ⇒ 8x = (10 * 24 ) ⇒ x= (10 * 24) /8 = 30min.
Q 4 - 8 men and 12 children can do a piece of work  in 9 days . A child takes double the time to do a work than the men. In how many days 12 men can complete the work?
A - 21/2 days
B - 14 days
C - 18 days
D - 27/2 days
2 children = 1 men ⇒ (8 men + 12 children ) = 14 men.
Let the required number of days be x. 
Less men , more day       (Indirect )
12 : 14:: 9 : x ⇒ 12x = ( 14 * 90 ⇒ ( 14* 9 ) /12 = 21 /2 = 21/2 days.
Q 5 - In a barrack of soldiers there was stock of food for 190 days for  4000 soldiers.After 30 days , 800 soldiers left the barrack. For how many days shall the left over Food last for the remaining soldiers?
A - 175 days
B - 200 days
C - 225 days
D - 250 days
Remaining food was sufficient for 4000 soldiers for 160 days.
Remaining   soldiers = ( 4000- 800) = 3200.
Let the required number of days  be x .
Less soldiers, more days    (Indirect)
3200 : 4000 :: 160  : x⇒ 3200 x = (4000 * 160 ) ⇒ x = (4000 * 160)/3200 = 200 days.
Q 6 - A contractor undertakes to build a wall in 50 days. He employs 50 people for the same . However,  after 25 days , he finds that only 40 % of the work is complete , How many more men need to  be employed to complete the work in time?
A - 20
B - 25
C - 30
D - 35
Work done = 40/100 = 2/5 , Remaining work = ( 1 - 2/5 ) = 3/5.
2/5 work is done in 25 days by 50 people.
3/5 work will be done in 25 days by (50 * 5/ 2 * 3/5) people = 75 people.
Required number of people = ( 75 ? 50 )  = 25.
Q 7 - 8 men working for 9 hours a day complete a piece of work in 20 days . In how many days can 7 men working for 10 hours a day complete the same piece of work?
A - 41/2 days
B - 103/5 days
C - 21 days
D - 144/7 days
Let the required number of days be x .
Less men , more days      ( Indirect)
More  working hours, less days      (Indirect)
Men    7: 8
:: 20 : x
Working hrs   10 : 9
∴ ( 7 * 10 * x ) = ( 8 * 9 * 20) ⇒ x = 8 * 9 * 20 / 7 * 10  = 144/7 = 144/7.
Q 8 - If 3 persons weave 336 shawls in 14 days , how many shawls will 8 persons weave in 5 days?
A - 180
B - 210
C - 252
D - 320
Let the required  number of  shawls be x.
More persons, more  shawls       (Direct)
Less days, less shawls         (Indirect)
Persons 3:8
:: 336 : x 
Days    14: 5 
∴ ( 3 * 14 * x ) = ( 8 * 5 * 336) ⇒ x = 8 * 5 * 336/ 3 * 14 = 320.
Q 9 - If 18 pumps can raise 2170 tonnes of water in 10 days , working 7 hours per day , in how many days will 16 pumps rise 1736 tonnes, working 9 hours per day?
A - 9 days
B - 8 days
C - 7 days
D - 6 days
Let the required number of days be x.
Less pumps, more days      (Indirect)
Less water, less days        (direct)
More working hrs, less days   (Indirect)
Pumps  16:18
Water Qty.     2170 : 1736          :: 10 :x
Water hrs     9:7
∴ (16 * 2170 * 9 *x ) =   ( 18 * 1736*7 *10)⇒ x=18 * 1736*7 *10/16*2170 * 9 = 7 days .
Q 10 - If x men working x hours per day can do x unit of work in x days , then y men working y hours per day would be able to do how much work in y days?
A - x2/y2 units
B - x3 / y2  unit
C - y2 / x3  unit
D - y3 / x2
More men , more work (Direct)
More working hrs , more work (Direct)
More days , more work (Direct)
Let the required work be z units. Then,
Men          x:y
working hrs       x:y                       :: x:z
days                x:y
∴ x*x*x*z = y * y* y* x ⇒ z= y3 / x2 units.