# 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?

A - 20 seconds

B - 15 seconds

C - 12 seconds

D - 10 seconds

### 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 - 3 men or 5 women can finish a piece of work in 12 days. How long will 6 men and 5 women take to finish the work?

A - 4 days

B - 10 days

C - 15 days

D - 20 days

### Explanation

```3 men = 5 women ⇒ 6 men =10 women
⇒ (6 men +5 women )= 15 women.
Let the required number  of days be x.
More women , less days      (Indirect)
15 : 5 :: 12 :  x ⇒ 15x = (5* 12 ) ⇒ x= (5*12)/15 = 4 days```

Q 3 - 10 women can complete a piece of work in 8 days and 10 children take 12 days to complete it. How many days will 6 women and 3 children together take to complete the work?

A - 9 days

B - 12 days

C - 10 days

D - 8 days

### Explanation

```1 women can complete the work in ( 10 * 8) = 80 days.
1 child can complete the work in ( 10 * 12) = 120 days.
1 women 1 days work = 1/80, 1 child 1 days work = 1/120.
( 6women  + 3 children) 1 days work = ( 6 * 1/80 + 3 * 1/120) = ( 3 /40 + 1/40 ) = 4/40=1/10.
Required time 10 days.```

Q 4 - A does half as much work as B in one- sixth of time. If together they take 10 days to complete the work, how much time shall B alone take to do it ?

A - 70 days

B - 40 days

C - 30 days

D - 20 days

### Explanation

```Suppose B takes x days to finish the work .
Then , A takes x/6 days to finish half the work .
∴ A takes 2x / 6 = x/3 days to finish the work.
1/x + 3/x = 1/10 ⇒ 4/x = 1/10 ⇒  x= 40.
Hence , B along takes 40 days to finish the work.```

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

### 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 contract is to be completed in 46 days and 117 men were set to works , each working 8 hours a day. After 33 days , 7/4 of the work is completed . How many additional men may be employed so that the work may be completed in time , each man now working 9 hours a days?

A - 80

B - 81

C - 82

D - 83

### Explanation

```Let the required number of men be x.
Work done = 4/7 , Remaining work  = ( 1- 4/7 ) = 3/7.
Less days , more  men           (Indirect)
More hrs/day, less men         (Indirect)
Less work , less men         ( Direct)
Days   13 : 33
Hrs/days    9:8 :: 117 : ( 117 +x)
Work:  4/7  :  3/7
∴ 13 * 9 * 4/7 * ( 117 + x) = 33 * 8 * 3/7* 117
⇒ ( 117 + x ) = 33 * 8 * 3 * 117/13 * 9 * 4 = 198 ⇒ x = ( 198 ? 117) = 81.```

Q 7 - If 5 spiders can catch 5 flies in 5 minutes, how many flies can 100 spiders catch in 100 minutes?

A - 100

B - 500

C - 1000

D - 2000

### Explanation

```Let the required number of flies be x.
More spiders , more flies      ( Direct)
More time, more flies             ( Direct)
Spiders    5 : 100
:: 5 : x
Times   5 : 100
( 5* 5 * x ) = ( 10 0* 100* 5 ) ⇒ x= 100 * 100* 5  / 5 * 5 = 2000 flies.```

Q 8 - In a hospital, there is a consumption of 1350 litres of milk for 70 patients for 30 days. How many patients will consume 1710 litres of milk in 28 days?

A - 59

B - 85

C - 95

D - 105

### Explanation

```Let the required number of patients be x .
More milk, more patients        (Direct)
Less days , more patients        (Indirect)
Litres   1350:1710
::70 : x
Days       28 : 30
∴ ( 1350 * 28 * x ) = ( 1710 * 30 * 70) ⇒ x= 1710 * 30 * 70/ ( 1350 * 28 ) = 95 patients.```

Q 9 - 2 men and 7 boys can do a piece of work in 14 days ; 3 men and 8 boys can do the same in 11 days . 8 men and 6 boys can do 3 times the amount of this work in

A - 21 days

B - 18 days

C - 24 days

D - 36 days

### Explanation

```Let 1 men 1 days work be 1/x and 1 boy 1 day work be 1/y
Then 2/x + 7/y = 1/14 ⇒ 2u + 7v = 1/14 -(i) When u= 1/x, v=1/y.
3/x +8/y =1/11 ⇒ 3u + 8v = 1/11?.(ii)
Multiplying (i) by (ii) by 2 and subtracting , we get:
5v = ( 3/14 ? 2/11) = 5/ 154 ⇒ v = 1/154
Putting v = 1/154 in (i) we get : 2u +7* 1/154 = 1/14
∴ 2u = (1/14- 1/22)= (11-7/54) = 4/154 = 2/77 ⇒ u=1/77.
(8 men +6 boys) 1 days work = (8/77 +6/154 ) = 22/154 = 1/7.
∴ 8men and 6 boys can do it in 7 days.
They will do thrice of this work in (3*7) days = 21days.```

Q 10 - A contractor undertakes to do a piece of work in 40 days . He engages 100 men at the beginning and 100 more after 35 days and complete the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?

A - 5

B - 6

C - 3

D - 9

```[(100 *35 ) + (200 *5)] men can finish the work in 1 day.