Arithmetic aptitude :: Allegation and Mixture :: Allegation and Mixture

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

Answer:

Explanation:

Let the veesel initially contain 8 litres

Let x litres of this liquid be replaced with water

Quantity of water in new mixture $=3-\frac{3x}{8}+x$

Quatity of syrup = $5-\frac{5x}{8}$

$3-\frac{3x}{8}+x=5+\frac{5x}{8}$ $\Rightarrow 5x+24=40-5x,x=\frac{8}{5}$

Part of mixture replaced $=\frac{8}{5}\times \frac{1}{8}=\frac{1}{5}$

In what ratio must a grocer mix two varieties of tea worth Rs.60 per kg and Rs.65 per kg.So that by selling the mixture at Rs.68.20 per kg he may gain 10%?

Answer:

Explanation:

S.P of 1 kg of mixture =Rs.68.20, Gain=10%

C.P of 1 kg of mixture  $=\frac{100}{110}\times 68.20=Rs.62$

By rule of alligation

Cost of 1 kg tea of 1st kind =Rs.60 +2 to mean price 60

Cost of 1 kg tea of 2nd kind =Rs.65 -3 to mean price 65

Required ratio = 3 : 2

A person has 1000 kg of sugar, part of which he sells at 8%profit and rest at 18% profit.He gains 14% on the whole .The quantity sold at 18% profit is 

Answer:

Explanation:

By the rule of alligation 

Profit of 1st part =8% which is +6 to mean profit 14%

Profit of 2nd part =18% which is -4 to mean profit 14%

Ratio of 1st and 2nd part = 4 : 6=2 : 3

Quantity of 2nd kind = $\frac{3}{5}\times 1000=600kg$

The cost of type 1 rice is Rs.15 per kg and type 2 rice is Rs.20 per kg.If both type1 and 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is 

Answer:

Explanation:

Let the price of mixed variety be =Rs.x

By the rule of alligation 

C.P of 1 kg of type 1 rice=Rs.15 ie x-15 to mean price Rs.x

C.P of 1 kg of type 2 rice=Rs.20 ie 20-x to mean price Rs.x

Given $\frac{20-x}{x-15}=\frac{2}{3}$

$\Rightarrow 60-3x=2x-30,x=18$

Price of the mixture is Rs. 18 per kg.

In what ratio must rice at Rs.9.30 per kg be mixed with rice at Rs.10.80 per kg.So that the mixture worth Rs.10per kg?

Answer:

Explanation:

By the rule of alligation 

C.P of 1 kg of 1st kind(in paise)=930 ie +70 to mean price 1000(in paise)

C.P of 1 kg of 2nd kind(in paise)=1080 ie -80 to mean price 1000(in paise)

Required ratio = 80 : 70 =8 : 7

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