5. Two solutions, the first of which contains 0.8 kg and the second 0.6 kg of salt, were poured together and 10 kg of a new salt solution was obtained. Find the weight of the first and of the second solution in the mixture if the first solution is known to contain 10 per cent more of salt than the second. (a) 4 kg, 6 kg (b) 3 kg, 7 kg (c) 4 kg, 9 kg (d) 5 kg, 9 kg
Answers
Weight of the first and of the second solution in the mixture are 4 kg and 6 kg respectively
Given : Two solutions, the first of which contains 0.8 kg and the second 0.6 kg of salt, were poured together and 10 kg of a new salt solution was obtained.
first solution is known to contain 10 per cent more of salt than the second
To Find : weight of the first and of the second solution in the mixture
Solution:
Assume that First solution = x kg
Second solution = 10 - x kg
Salt in 2nd solution = 0.6 kg
in % = ( 0.6 / (10-x)) * 100 = 60/(10 - x) %
1st solution % = (60/(10 -x)) + 10 % as contain 10 per cent more of salt than the second.
(0.8/x) * 100 = 80/x %
Equate both
80/x = (60/(10 -x)) + 10
=> 8/x = (6/(10 -x)) + 1
=> 8(10 - x) = 6x + x(10 - x)
=> 80 - 8x = 6x + 10x - x²
=> x² -24x + 80 = 0
=> x² - 20x - 4x + 80 = 0
=> (x - 20)(x - 4) = 0
=> x = 20 , x = 4
as x < 10
Hence x = 4 kg
10 - x = 6 kg
Correct option is a) 4 kg , 6 kg
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Answer:
Step-by-step explanation: