57
Q:

A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

A) 1/3 B) 1/4
C) 1/5 D) 1/7

Answer:   C) 1/5

Explanation:

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.
Quantity of water in new mixture =  litres.

Quantity of syrup in new mixture =   litres.

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=>   5x + 24 = 40 - 5x 

=>   10x = 16    => x = 8/5

So, part of the mixture replaced =  = 1/5.

Q:

A Container has a capacity of 48 litres and is full of milk. 4 liters of milk is taken out of it and replaced by same quantity of water. Again 4 liters of the mixture is taken out and replaced by the same quantity of water . The process is repeated five times. How much milk is left in the mixture ?

Answer

 = 



Milk left in the container = 



 =  liters

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8 462
Q:

In what proportion water must be added to spirit to gain 20% by selling it at the cost price ?

Answer

Let the C.P of spirit be = Rs.10 per litre


S.P of the mixture = Rs. 10 per litre


Profit = 20


 C.P of the mixture = Rs.  = Rs.  per litre




Ratio of water and spirit = 1 : 5

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4 1221
Q:

A sum of Rs.118 was divided among 50 boys and girls such that each boy received Rs.2.60 and each girl Rs.1.80. Find the number of boys and girls ?

Answer

Average money received by each =  = Rs. 2.36



Ratio of No.of boys and girls = 56 : 24 = 7 : 3


 Number of boys =  = 35


Number of girls = 50 - 35 = 15

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10 873
Q:

A man travelled a distance of 80 km in 7 hours partly on foot at the rate of 8 km per hour and partly on bicycle at 16 km /hr. Find the distance travelled on foot ?

Answer



Thus out of 7 hrs in all, he took 4 hrs to travel on foot 


 Distance covered on foot in 4 hrs = ( 4 x 8) = 32 km

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6 1009
Q:

In what ratio should two varieties of tea at Rs. 60 per kg and Rs.120 per kg be mixed together so that by selling the mixture at Rs.96 per kg, a profit of Rs.20% is obtained ?

Answer

Let us first calculate the cost of price of the mixture. the selling price of the mixture is given as Rs.96 and the profit is given as 20%. So, Cost price =  = Rs. 80


Now, let us apply allegation method :



= 40 : 20 =  2 : 1

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7 274