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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

Q:

From a tank of petrol , which contains 200 liters of petrol, the seller replaces each time with kerosene when he sells 40 liters of petrol(or mixture). Everytime he sells out only 40 liters of petrol (pure or impure). After replacing the petrol with kerosene 4th time, the total amount of kerosene in the mixture is

A) 81.92L	B) 96L
C) 118.08L	D) None of these

Answer & Explanation Answer: C) 118.08L

Explanation:

The amount of petrol left after 4 operations = $200 \times {(1 - \frac{40}{200})}^{4} =$ 81.92

Hence the amount of kerosene = 200 - 81.92 = 118.08 liters

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Filed Under: Alligation or Mixture

Q:

From the 50 liters of milk, 5 liters of milk is taken out and after it 5 liters of water is added to the rest amount of milk. Again 5 liters of milk and water is drawn out and it was replaced by 5 liters of water. If this process is continued similarly for the third time, the amount of milk left after the third replacement:

A) 45L	B) 36.45L
C) 40.5L	D) 42.5L

Answer & Explanation Answer: B) 36.45L

Explanation:

General Formula:

Final or reduced concentration = initial concentration x ${(1 - \frac{a m o u n t b e i n g r e p l a c e d i n e a c h o p e r a t i o n}{t o t a l a m o u n t})}^{n}$

where n is the number of times the same operation is being repeated. The "amount being replaced" could be pure or mixture as per the case. similarly ,"total amount" could also be either pure or mixture. Here amount being replaced denotes the quantity which is to be withdrawn in each time.

Therefore, $50 \times {(1 - \frac{5}{50})}^{3}$

= 36.45 L

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Filed Under: Alligation or Mixture

Q:

In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?

A) 1:4	B) 1:3
C) 2:3	D) 3:4

Answer & Explanation Answer: B) 1:3

Explanation:

33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3

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Filed Under: Profit and Loss

Q:

A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:

A) 29	B) 37
C) 42	D) 54

Answer & Explanation Answer: C) 42

Explanation:

After 10 days : 150 men had food for 35 days.

Suppose 125 men had food for x days.

Now, Less men, More days (Indirect Proportion)

$∴$ 125 : 150 :: 35 : x $\Leftrightarrow$ 125 x x = 150 x 35

$\Rightarrow x = \frac{150 \times 35}{125} = 42$

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Filed Under: Chain Rule

Q:

A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

A) Rs. 7500	B) Rs. 8000
C) Rs. 8500	D) Rs. 9000

Answer & Explanation Answer: D) Rs. 9000

Explanation:

Let B's capital be Rs. x.

Then, $[\frac{3500 \times 12}{7 x} = \frac{2}{3}]$

=> 14x = 126000

=> x = 9000.

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Filed Under: Partnership

Q:

A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?

A) 100 m	B) 150 m
C) 190 m	D) 200 m

Answer & Explanation Answer: A) 100 m

Explanation:

Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr

Distance covered in 6 minutes = (1/60) x 6 km = 1/10 km = 100 m

Therefore, Distance between the thief and policeman = (200 – 100) m = 100 m.

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Filed Under: Time and Distance

Q:

The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?

A) 456 kms	B) 482 kms
C) 552 kms	D) 556 kms

Answer & Explanation Answer: C) 552 kms

Explanation:

Total distance travelled in 12 hours =(35+37+39+.....upto 12 terms)
This is an A.P with first term, a=35, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 35+{12-1) x 2]
=6(70+23)
= 552 kms.

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Filed Under: Time and Distance

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