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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 - If 4/5th of a cistern is filled in 1 minute, how much more time will be required to fill the rest of it?
Answer : B
Explanation
Let the required time be x seconds. Part filled = 4/5, Remaining part = (1- 4/5 ) = 1/5. Less part to be filled , less is the time taken (direct) 4/5 :1/5 :: 60 : x ⇒ 4/5 * x = (1/5 * 60 ) = 12 ⇒ x= (12 * 5/4 ) = 15. Required time = 15 seconds.
Q 2 - A tree 6m tall casts a 4m long shadow. At the same times, a flagpole casts a 50 m long shadow. How long is the flagpole?
Answer : B
Explanation
Let the length of the flagpole be x metres. Longer is the shadow, longer is the object (Direct) 4: 50 :: 6:x ⇒ 4x = (50 * 6 ) ⇒ x= (50*6 )/4 =75m. Length of flagpole = 75m.
Q 3 - If 12 men or 18 women can do a piece of work in 14 days , how long will 8 men and 16 women take to finish the work?
Answer : A
Explanation
12 men = 18 women ⇒ 1 man = 18/12 women ⇒ 8 men = (18/12 * 8) women = 12 women ⇒ (8 men + 16 women ) = 28 women Let the required number of days be x. More women, less days (Indirect) 28: 18:: 14 : x ⇒ 28x = (18*14 ) ⇒ x= (18 *14) / 28 = 9days
Q 4 - A man and a boy working together can complete a work in 24 days . If for the last 6 days man alone the work , then it is completed in 26 days. How long will the boy take to complete the work alone?
Answer : A
Explanation
Let 1 men 1 days work be 1/x and 1 boy 1 days work be 1/y Then, 1/x + 1/y = 1/24 20/x + 20 / y + 6 /x )1 ⇒ 20 (1/x + 1/y) + 6/x = 1 ⇒ (20 * 24) + 6/x = 1 ⇒ 6/x = (1- 20/24) = 4 / 24 = 1/6 ⇒ 1/x = 1/ 36 ⇒ 1/y = ( 1/24 - 1/ 36 ) = 1/72. ∴ The boy along will do it in 72 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?
Answer : B
Explanation
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 garrison of 3300 men had provisions for 32 days , when given at the rate of 850 gm per head . At the end of 7 days , a reinforcement arrived and it was found that the provisions would last 17 days more , when given at the rate of 825 gm per head . What was the strength of the reinforcement?
Answer : C
Explanation
Let the required strength of reinforcement be x. 3300 men had provisions for (32-7 ) = 25 days. Less food per head , more persons (Indirect) Less days , more persons (Indirect) Food per days 825 : 850 :: 3300 : (3300 x ) Days 17 : 25 ∴ 825 * 17 * (3300 + x ) = 850 * 25 * 3300 ⇒ ( 3300 + x ) = 850 * 25 * 3300/825 * 17 = 5000 ⇒ x = ( 5000 - 3300) = 1700 men.
Q 7 - 400 persons working 9 hours per day complete 1/4 th of the work in 10 days . The number of additional persons , working 8 hours per day required to complete the remaining work in 20 days , is:
Answer : D
Explanation
Let the number of additional men be x . Less hrs per days, more men ( Indirect) More days , less men ( Indirect) More work, more men ( Direct) Her/ days 8:9 Days 20 : 10 :: 400 : ( 400 + x ) Work 1/4 : 3/4 ∴ 8 * 20 * 1/4 * ( 400 + x ) = 9 * 10 * 3/4 * 400 ⇒ ( 400 + x ) = 9 * 10 * 3 * 400/ 8 * 20 = 675. Number of additional men = 675.
Q 8 - If the rent for grazing 40 cows for 20 days in Rs 740, how many cows can graze for 30 days on Rs 222?
Answer : B
Explanation
Let the required number of cows be x. Less rent, less cows (Direct) More days, less cows (Indirect) Rent 740 : 222 :: 40 : x Days 30: 20 ∴ ( 740 * 30 * x) = ( 222 * 20 * 40 ) ⇒ x = 222* 20 * 40 / 740 * 30 = 8 cows.
Q 9 - A contractor employed 30 men to do a piece of work in 38 days. After 25 days he employed 5 men more and the work was finished one day earlier. How many days , he would have been behind , if he had not employed additional men?
Answer : A
Explanation
After 25 days , 35 men finish the remaining work in (38 - 25 - 1) = 12 days. 35 men can finish the remaining work in 12 days. 30 men can finish it in (12 * 35) /30 days = 14 days , i.e. 1 day behind.
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?
Answer : D
Explanation
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.