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April 13th, 2018, 02:14 AM   #1
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When should we draw alligations diagram?

1) Two vessels A and B contains 80% and 75% of alcohol respectively. Ten litres of solution from A is mixed with 20 litres of solution from B. What is the ratio of alcohol of water in the mixture?

Solution: Quantity of alcohol in the mixture

= $10\dfrac{80}{100} + 20\dfrac {75}{100}$

= 8 + 15 = 23 litres.

30 - 23 = 7 litres

The ratio of alcohol to water in the mixture = 23 : 7.

2) A Certain variety of rice which costs 32 /- per kg is mixed with 12 kg of another variety of rice which costs 40 per kg and the mixture is sold at 49 per kg gaining a profit of 40%. Find the quantity of the mixture.

Solution: Let the cost price of the mixture per kg be C.

$C\times\dfrac {100+40}{100} = 49$

C = 35

So the ratio of the quantities of the first variety that of the second variety = 5: 3

The quantity of mixture = $\displaystyle 12\times\dfrac{8}{3} = 32$

In first problem, alligations diagram is not drawn but in second problem, it is drawn. please tell when should we draw alligations diagram?

Last edited by Ganesh Ujwal; April 13th, 2018 at 02:21 AM.
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