Question

A Container Contains mixture of wine and water in the ratio of 7:x. 64 litres litres of
of mixture is taken out of the container and replaced with 39 litres of wine so that the ratio of wine water in the container becomes 3:2. find the value of x, if the initial quantity of wine in the container is 70 litres. ​

Answer 1

Answer:

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Answer 2

Given :  A Container Contains mixture of wine and water in the ratio of 7:x .  64 litres  of  of mixture is taken out of the container and replaced with 39 litres of wine

ratio of wine water in the container becomes 3:2.

initial quantity of wine in the container is 70 litres. ​

To Find  : the value of x,

Solution:

mixture of wine and water in the ratio of 7: x  

Wine = 70 Litre

Water = 10x

Total = 70 + 10x Litre

64 litres of  of mixture is taken out of the container and replaced with 39 litres of wine

64 litres  contains  Wine  = (70/(70 + 10x))* 64  = 448/(7 + x)

64 litres  contains  Water  = (10x/(70 + 10x))* 64  =64x/(7 + x)

wine in new mixture =   70 - 448/(7 + x) + 39  = 109 - 448/(7 + x)  = (763 + 109x - 448)/(7 + x)  =  ( 315 + 109x)/(7 + x)

water in new mixture = 10x - 64x/(7 + x)   = ( 70x + 10x² - 64x)/(7 + x)

= (10x² + 6x)/(7 + x)

ratio of wine water in the container becomes 3:2

= ( 315 + 109x)/(7 + x)  :  (10x² + 6x)/(7 + x) =  3: 2

=> 2 ( 315 + 109x) = 3 (10x² + 6x)

=> 30x² + 18x  - 218x  - 630 = 0

=> 30x² - 200x - 630 =0

=> 3x² - 20x - 63 = 0

=> 3x² - 27x + 7x - 63 = 0

=> 3x(x - 9) + 7(x - 9) = 0

=> (3x + 7)(x - 9) = 0

=> x = 9

Verification :

initially

Wine  Water

70  :   90

64 litre has   Wine = 28 and water 36 litre

Wine = 70 - 28 + 39 = 81

Water = 90 - 36  = 54

81 : 54

= 3 : 2

value of x = 9

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