# Chain Rules - Online Quiz

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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 21 cows eat as much as 15 buffaloes, how many cows will eat as much as 35 buffaloes?

A - 49

B - 56

C - 45

D - 47

### Explanation

```15 buffaloes = 21 cows ⇒ 1 buffalo = 21/15 cows = 7/5 cows
⇒35 buffaloes = (35 * 7/5 ) cows = 49 cows.```

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 - 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?

A - 9 days

B - 10 days

C - 12 days

D - 14 days

### 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 - 8 men can finish a piece of work in 40 days . If 2 more men join with them , then the work will be completed in?

A - 30 days

B - 32 days

C - 36 days

D - 25 days

### Explanation

```Let  10 men finish it in x days.
More men, less days     (Indirect)
10 : 8 :: 40 : x ⇒ 10x = (8 * 40 ) ⇒ x = (8*40) /10 = 32 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

### 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 - Four examiners can examine a certain number of answer papers in 10 days by working for 5 hours a day. For how many hours in a day would 2 examiners have to work in order to examine twice the number of answer papers in 20 days?

A - 15/2 hours

B - 8 hours

C - 7/2 hours

D - 10 hours

### Explanation

```Let the number of hours per days be x.
More days, less hours per days          ( Indirect)
Less examiners , more hours per days         ( Indirect)
More Ans. Books , more hours per days     ( direct)
Days         20 : 10
Examiners      2 : 4 :: 5 : x
Ans. Books   1 : 2
∴ (20 * 2 * 1 * x) = ( 10 * 4 * 2* 5 ) ⇒ x = 400 / 40 = 10 hrs per days.```

Q 7 - Running at the same constant rate , 6 identical machines can produce 2700 bottle per minute . At this rate , how many bottles could 10 such machines produce in 4 minutes?

A - 648

B - 1800

C - 2700

D - 10800

### Explanation

```Let the required number  of bottles be x .
More machines, more bottles    ( Direct)
More time, more bottles      ( Direct)
Machines         6 : 10
:: 2700 : x
Time     1:4
(6 * 1 * x) = 10 * 4 * 2700 ) ⇒ 10 * 4 * 2700 / 6 = 1800 bottles.```

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?

A - 6

B - 8

C - 5

D - 12

### 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 - 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 - 20 men complete one third of a piece of work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days?

A - 10

B - 12

C - 15

D - 20

### Explanation

```Work done = 1/3, Remaining work = (1- 1/3 ) = 2/3
Let the number of additional men be x.
More work, more men      (Direct)
More days , less men         (Indirect)
Work 1/3 : 2 /3
:: 20 : (20 +x)
Days 25:20
1/3 * 25 * ( 20 + x) = 2 /3 * 20 *20 ⇒ (20 +x) = 32 ⇒ x=12.
Required number of days  = 12.```

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