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Q:

In a public bathroom there are n taps 1,2,3...n. Tap1 and Tap2 take equal time to fill the tank while Tap3 takes half the time taken by Tap2 and Tap4 takes half the time taken by Tap3. Similarly each next number of tap takes half the time taken by previous number of Tap i.e, K-th Tap takes half the time taken by (K-1)th Tap. If the 10th tap takes 2 hours to fill the tank alone then what is the ratio of efficiency of 8th tap and 12th tap, respectively?

A) 4:1	B) 5:3
C) 16:1	D) 1:16

Answer & Explanation Answer: D) 1:16

Explanation:

Time taken by 8th tap = 2 x 2 x 2= 8 hours

Time taken by 12th tap = 2x (1/2) x (1/2) = 1/2 hour

Ratio of time taken by 8th tap and 12th tap = 8 : 1/2 =16:1

Therefore, Ratio of efficiencies of 8th tap and 12th tap =1:16

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Filed Under: Time and Work

Q:

A Contractor employed a certain number of workers to finish constructing a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the road on the scheduled time. How much work he had been completed, before increasing the number of workers?

A) 10 %	B) 14 ( 2/7 )%
C) 20 %	D) Can't be determined

Answer & Explanation Answer: B) 14 ( 2/7 )%

Explanation:

Let he initially employed x workers which works for D days and he estimated 100 days for the whole work and then he doubled the worker for (100-D) days.

D * x +(100- D) * 2x= 175x

=> D= 25 days

Now , the work done in 25 days = 25x

Total work = 175x

Therefore, workdone before increasing the no of workers = $\frac{25 x}{175 x} \times 100$ % = $14 \frac{2}{7} %$

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Filed Under: Time and Work

Q:

A single reservoir supplies the petrol to the whole city, while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume. When the reservoir is full and if 40,000 liters of petrol is used daily, the suply fails in 90 days.If 32,000 liters of petrol is used daily, it fails in 60 days. How much petrol can be used daily with out the supply ever failing?

A) 64000 liters	B) 56000 liters
C) 78000 liters	D) 60000 liters

Answer & Explanation Answer: B) 56000 liters

Explanation:

Let x liter be the per day filling and v litr be the capacity of the reservoir, then

90x + v = 40000 * 90 -----(1)

60x + v= 32000 * 60 ------(2)

solving eq.(1) and (2) , we get

x = 56000

Hence , 56000 liters per day can be used without the failure of supply.

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Filed Under: Time and Work

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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Filed Under: Time and Work

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:

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:

The diluted wine contains only 8 liters of wine and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing wine. How many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water in the mixture ?

A) 4	B) 5
C) 8	D) None of these

Answer & Explanation Answer: B) 5

Explanation:

Wine Water

8L 32L

1 : 4

20 % 80% (original ratio)

30 % 70% (required ratio)

In ths case, the percentage of water being reduced when the mixture is being replaced with wine.

so the ratio of left quantity to the initial quantity is 7:8

Therefore , $\frac{7}{8} = [1 - \frac{K}{40}]$

=> K = 5 Lit

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Filed Under: Alligation or Mixture
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