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03 Apr 2020, 06:07
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
51% (03:11) correct
49%
(03:06)
wrong
based on 193
sessions
History
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Two types of tea, A and B, are mixed and then sold at $40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio
A. 21 : 25
B. 19 : 24
C. 18 : 25
D. 17 : 25
E. 13 : 25
Are You Up For the Challenge: 700 Level Questions
A. 21 : 25
B. 19 : 24
C. 18 : 25
D. 17 : 25
E. 13 : 25
Are You Up For the Challenge: 700 Level Questions
03 Apr 2020, 09:40
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Bunuel
Let the Cost price of tea A & B be '\(a\)' & '\(b\)' respectively
The profit is 10% if A and B are mixed in the ratio 3 : 2
--> Fraction of tea A & B = \(\frac{3a}{5}\) & \(\frac{2b}{5}\)
Also, SP = 110% of CP
--> \(40 = \frac{110}{100}*\frac{(3a + 2b)}{5}\) ....... (1)
The profit is 5% if A and B are mixed in the ratio 2 : 3
--> Fraction of tea A & B = \(\frac{2a}{5}\) & \(\frac{3b}{5}\)
SP = 105% of CP
--> \(40 = \frac{105}{100}*\frac{(2a + 3b)}{5}\) ....... (2)
From (1) & (2),
\(\frac{110}{100}*\frac{(3a + 2b)}{5} = \frac{105}{100}*\frac{(2a + 3b)}{5}\)
--> \(110(3a + 2b) = 105(2a + 3b)\)
--> \(22(3a + 2b) = 21(2a + 3b)\)
--> \(66a + 44b = 42a + 63b\)
--> \(24a = 19b\)
-->\(\frac{a}{b} = \frac{19}{24}\)
Option B
General Discussion
03 Apr 2020, 14:36
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The selling price of the mixture is Rs. 40/kg.
Let a be the quantity of tea A in the mixture and b be the quantity of tea B in the mixture.
The profit is 10% if the two varieties are mixed in the ratio 3 : 2.
Let the cost price of the mixture be x.
So, 1.1x = 40
x = 40/1.1
(3a + 2b)/5 = 40/1.1
3.3a + 2.2b = 200
The profit is 5% if the two varieties are mixed in the ratio 2 : 3.
(2a + 3b)/5 = 40/1.05
2.1a + 3.15b = 200
Equating both the equations, we get
3.3a + 2.2b = 2.1a + 3.15b
1.2a = 0.95b
a/b = 0.95/1.2
a/b = 19/24
The correct option is B.
Let a be the quantity of tea A in the mixture and b be the quantity of tea B in the mixture.
The profit is 10% if the two varieties are mixed in the ratio 3 : 2.
Let the cost price of the mixture be x.
So, 1.1x = 40
x = 40/1.1
(3a + 2b)/5 = 40/1.1
3.3a + 2.2b = 200
The profit is 5% if the two varieties are mixed in the ratio 2 : 3.
(2a + 3b)/5 = 40/1.05
2.1a + 3.15b = 200
Equating both the equations, we get
3.3a + 2.2b = 2.1a + 3.15b
1.2a = 0.95b
a/b = 0.95/1.2
a/b = 19/24
The correct option is B.
