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Q:

A is twice efficient as B and together they do the same work in as much time as C and D together. If C and D can complete the work in 20 and 30 daysrespectively, working alone ,then in how many days A can complete the work individually:

A) 12 days	B) 18 days
C) 24 days	D) 30 days

Answer & Explanation Answer: B) 18 days

Explanation:

A + B = C + D

| | | |

Ratio of efficiency 10x + 5x 9x + 6x

|________| |_________|

15x 15x

Therefore , ratio of efficiency of A:C =10:9

Therefore, ratio of days taken by A:C = 9:10

Therefore, number of days taken by A = 18 days

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Q:

The ratio of efficiency of A is to C is 5:3. The ratio of number of days taken by B is to C is 2:3. A takes 6 days less than C, when A and C completes the work individually. B and C started the work and left after 2 days. The number of days taken by A to finish the remaining work is:

A) 4.5	B) 5
C) 6	D) 9 1/3

Answer & Explanation Answer: C) 6

Explanation:

A : C

Efficiency 5 : 3

No of days 3x : 5x

Given that, 5x-6 =3x => x = 3

Number of days taken by A = 9

Number of days taken by C = 15

B : C

Days 2 : 3

Therefore, Number of days taken by B = 10

Work done by B and C in initial 2 days = $2 [\frac{1}{10} + \frac{1}{15}]$ = 1/3

Thus, Rest work =2/3

Number of days required by A to finish 2/3 work = (2/3) x 9 = 6 days

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Q:

A is thrice efficient as B and C is twice as efficient as B. what is the ratio of number of days taken by A,B and C, when they work individually?

A) 2:6:3	B) 2:3:6
C) 1:2:3	D) 3:1:2

Answer & Explanation Answer: A) 2:6:3

Explanation:

A : B : C

Ratio of efficiency 3 : 1 : 2

Ratio of No.of days 1/3 : 1/1 : 1/2

or 2 : 6 : 3

Hence A is correct.

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Filed Under: Time and Work

Q:

Application of Inverse Proportion

If 20 persons can do a piece of work in 7 days then calculate the number of persons require to complete the work in 28 days

Answer

Number of persons * days = work

20 * 7 = 140 man- days

Now, x * 28 = 140 men- days

=> x =5

Therefore in second case the required number of person is 5.

Second method:

Since work is constant, therefore M1 x D1= M2 x D2

20 x 7 = M2 x 28

=> M2 = 5

Workspace

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Subject: Time and Work

Q:

Concept of Nehative Work

A tub can be filed in 20 minutes but there is a lekage in it which can empty the full tub in 60 minutes. In how many minutes it can be filled?

Answer

Filling efficiency = 5%

Emptying efficiency = 1.66%

Net efficiency = 5-1.66 = 3.33%

Therefore, Required time to fil the tub =100/3.33= 30 minutes

Workspace

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Subject: Time and Work

Q:

From a container, 6 liters milk was drawn out and was replaced by water. Again 6 liters of mixture was drawn out and was replaced by the water. Thus the quantity of milk and water in the container after these two operations is 9:16. The quantity of mixture is:

A) 15	B) 16
C) 25	D) 31

Answer & Explanation Answer: A) 15

Explanation:

Let quantity of mixture be x liters.

Suppose a container contains x units of liquid from which y units are taken out and replaced by Water. After operations , the quantity of pure liquid = $x {(1 - \frac{y}{x})}^{n}$ units, Where n = no of operations .

So, Quantity of Milk = $x {(1 - \frac{6}{x})}^{2}$

Given that, Milk : Water = 9 : 16

=> Milk : (Milk + Water) = 9 : (9+16)

=> Milk : Mixture = 9 : 25

Therefore, $\frac{x {(1 - \frac{6}{x})}^{2}}{x} = \frac{9}{25}$

=> x = 15 liters

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Filed Under: Alligation or Mixture

Q:

The ratio of petrol and kerosene in the container is 3:2 when 10 liters of the mixture is taken out and is replaced by the kerosene, the ratio become 2:3. Then total quantity of the mixture in the container is:

A) 25	B) 30
C) 45	D) cannot be determined

Answer & Explanation Answer: B) 30

Explanation:

pool : kerosene

3 : 2(initially)

2 : 3(after replacement)

$\frac{R e m a i n i n g Q u a n t i t y}{I n i t i a l Q u a n t i t y} = (1 - \frac{R e p l a c e d Q u a n t i t y}{T o t a l Q u a n t i t y})$

(for petrol) $\frac{2}{3} = (1 - \frac{10}{k})$

=> K = 30

Therefore the total quantity of the mixture in the container is 30 liters.

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Filed Under: Alligation or Mixture

Q:

In a mixture of milk and water, there is only 26% water. After replacing the mixture with 7 liters of pure milk , the percentage of milk in the mixture become 76%. The quantity of mixture is:

A) 65 liters	B) 91 liters
C) 38 liters	D) None of these

Answer & Explanation Answer: B) 91 liters

Explanation:

Milk Water

74% 26% (initially)

76% 24% ( after replacement)

Left amount = Initial amount $(1 - \frac{r e p l a c e d a m o u n t}{t o t a l a m o u n t})$

24 = 26 $(1 - \frac{7}{k})$

=> k = 91

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Filed Under: Alligation or Mixture

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