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07 Oct 2018, 06:53
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ALLEGATION FORMULA DERIVATION:
C/D=D-M/M-C
Quantity of cheaper/Quantity of dearer
=CP of dearer - Mean Price/Mean price - CP of cheaper
Let cost price of unit quantity of cheaper ingredient = c
cost price of unit quantity of dearer ingredient = d
Suppose 'a' units of cheaper ingredient and 'b' units of dearer ingredient are mixed.
Total quantity of the mixture = a + b
Total cost price of the mixture = (ac + bd)
cost price of unit quantity of the mixture (mean price) =
ac + bd/a+b
Suppose mean price = m
=>
ac + bd/a+b =m (1)
Now cross multiply perform on (1)
=> am + bm = ac + bd
=> am - ac = bd - bm
=> a(m - c) = b(d -m)
=> a/b = (d -m)/(m - c)
=> a : b = (d -m):(m - c)
In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
A. 3 : 7
B. 5 : 7
C. 7 : 3
D. 7 : 5
C/D=D-M/M-C
C/D= 20-16.50/16.50-15
=3.50/1.50 =7:3
FORMULA 2-MULTIPLE REPLACEMENT IN MIXTURE:
Let us describe this formula through the application
A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?
A. 17 : 3
B. 9 : 1
C. 3 : 17
D. 5 : 3
E. 4 : 6
We are essentially replacing water in the mixture with pure milk.
Let W1 be the amount of water in the mixture originally = 8 litres.
Let WR be the amount of water in the mixture after the replacements have taken place.
Then, WR/W1 = (1−R/M)^n
where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.
Hence, WR/W1 = (1−10/20)^2 = 1/4
Therefore, WR = W1/4 = 8/4 = 2 litres.
WR is the quantity of water in the mixture after the process is done twice.
So, the final quantity of water in the 20-litre mixtures is 2 litres.
Hence, the mixture will have 18 litres of milk and 2 litres of water.
So ratio is 18:2=9:1
C/D=D-M/M-C
Quantity of cheaper/Quantity of dearer
=CP of dearer - Mean Price/Mean price - CP of cheaper
Let cost price of unit quantity of cheaper ingredient = c
cost price of unit quantity of dearer ingredient = d
Suppose 'a' units of cheaper ingredient and 'b' units of dearer ingredient are mixed.
Total quantity of the mixture = a + b
Total cost price of the mixture = (ac + bd)
cost price of unit quantity of the mixture (mean price) =
ac + bd/a+b
Suppose mean price = m
=>
ac + bd/a+b =m (1)
Now cross multiply perform on (1)
=> am + bm = ac + bd
=> am - ac = bd - bm
=> a(m - c) = b(d -m)
=> a/b = (d -m)/(m - c)
=> a : b = (d -m):(m - c)
In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
A. 3 : 7
B. 5 : 7
C. 7 : 3
D. 7 : 5
C/D=D-M/M-C
C/D= 20-16.50/16.50-15
=3.50/1.50 =7:3
FORMULA 2-MULTIPLE REPLACEMENT IN MIXTURE:
Let us describe this formula through the application
A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?
A. 17 : 3
B. 9 : 1
C. 3 : 17
D. 5 : 3
E. 4 : 6
We are essentially replacing water in the mixture with pure milk.
Let W1 be the amount of water in the mixture originally = 8 litres.
Let WR be the amount of water in the mixture after the replacements have taken place.
Then, WR/W1 = (1−R/M)^n
where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.
Hence, WR/W1 = (1−10/20)^2 = 1/4
Therefore, WR = W1/4 = 8/4 = 2 litres.
WR is the quantity of water in the mixture after the process is done twice.
So, the final quantity of water in the 20-litre mixtures is 2 litres.
Hence, the mixture will have 18 litres of milk and 2 litres of water.
So ratio is 18:2=9:1
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07 Oct 2020, 23:13
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Hi there,
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Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
