qa02 mixtures
TRANSCRIPT
QA02 MIXTURES / ALLIGATIONS
Alligation• It is the rule that enables us • to find the ratio in which two or more ingredients
at the given price • must be mixed to produce a mixture• of desired price.
Mean Price• The cost of a unit quantity of the mixture is called
the mean price
Rule of Alligation• If two ingredients are mixed, then • C.P of a unit quantity of cheaper = (c) • C.P of a unit quantity of dearer = (d)
C D
D–M
M–C
Mean Price (m)
• 2.In what ratio must a grocer mix two varieties of pulses costing `.15 and `.20 per kg respectively so as to get a mixture worth `.16.50 kg?
First type Mean Price Second type15 16.50 203.50 1.50
3.501.50=
3515=
73
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• 4. A jar full of whisky contains 40% alcohol. A part
of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:
First Mean Price Second type40% 26% 19%7 14
The ratio is 7:14 = 1:2. Hence quantity replaced =
04
• 5.In what ratio must water be mixed with milk to gain on selling the mixture at cost price?
• Let C.P. of 1 litre milk be Re. 1.• S.P. of 1 litre of mixture = Re.1, • C.P. of 1 litre of mixture =
First type Mean Price Second type0 1
Ratio of water and milk = 1:6.
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• If n different vessels of equal size are filled with the mixture of P and Q in the ratio p1 : q1, p2 : q2, ……, pn : qn and content of all these vessels are mixed in one large vessel, then
Quantity of PQuantity of Q
=
p1p1+q1
+p2
p2+q2+…+
pnpn+qn
q1p1+q1
+q2p2+q2
+…+q𝑛p𝑛+qn
• Three equal buckets containing the mixture of milk and water are mixed into a bigger bucket.
• If the proportion of milk and water in the glasses are 3:1, 2:3 and 2:1 then find the proportion of milk and water in the bigger bucket.Let’s say P stands for milk and Q stands for water,So, p1:q1 = 3:1p2:q2=2:3p3 : q3=2:1
So in bigger bucket,Milk : Water = 109 : 71
𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦𝑜𝑓 𝑀𝑖𝑙𝑘𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑜𝑓 𝑊𝑎𝑡𝑒𝑟=
33+1 +
22+3 +
22+1
13+1
+ 32+3
+ 12+1
𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦𝑜𝑓 𝑀𝑖𝑙𝑘𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑜𝑓 𝑊𝑎𝑡𝑒𝑟=
10971
• If n different vessels of sizes x1, x2, …, xn are filled with the mixture of P and Q in the ratio p1 : q1, p2 : q2, ……, pn : qn and content of all these vessels are mixed in one large vessel, then
Quantity of PQuantity of Q
=
p1𝑥1p1+q1
+p2𝑥2p2+q2
+…+pn𝑥𝑛
pn+qnq1 𝑥1p1+q1
+q2 𝑥2p2+q2
+…+q𝑛𝑥𝑛
p𝑛+qn
• Three buckets of size 2 litre, 4 litre and 5 litre containing the mixture of milk and water are mixed into a bigger bucket. If the proportion of milk and water in the glasses are 3:1, 2:3 and 2:1 then find the proportion of milk and water in the bigger bucket.Sol:
• Let’s say P stands for milk and Q stands for water,So, p1:q1 = 3:1 , x1 = 2p2:q2=2:3 , x2 = 4p3 : q3=2:1 x3 = 5, so
So in bigger bucket,Milk : Water = 193 : 137
𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦𝑜𝑓 𝑀𝑖𝑙𝑘𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑜𝑓 𝑊𝑎𝑡𝑒𝑟=
3 𝑋 23+1 +
2𝑋 42+3 +
2 𝑋 52+1
1𝑋 23+1
+ 3 𝑋 42+3
+ 1 𝑋 52+1
𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦𝑜𝑓 𝑀𝑖𝑙𝑘𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑜𝑓 𝑊𝑎𝑡𝑒𝑟=
193137
Quantity of PQuantity of Q
=
p1𝑥1p1+q1
+p2𝑥2p2+q2
+…+pn𝑥𝑛
pn+qnq1 𝑥1p1+q1
+q2 𝑥2p2+q2
+…+q𝑛𝑥𝑛
p𝑛+qn
• Suppose a container contains x of liquid from which y units are taken out and replaced by water. After n operations, the quantity of pure liquid = units.
• A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
• Milk =
• p gram of ingredient solution has a% ingredient in it.
• To increase the ingredient content to b% in the solution
• Quantity of ingredient need to be added = • 125 litre of mixture of milk and water
contains 25% of water. How much water must be added to it to make water 30% in the new mixture?Sol:
• Let’s say p = 125, b = 30, a = 25So from the equation
• 8.92 litres.
• If in x litres mixtures of milk and water, the ratio of milk and water is a:b, the quantity of water to be added in order to make this ratio c:d is
1. In a mixture of 60 litres, the ratio of milk and water is 2:1. If this ratio is to be 1:2, then the quantity of water to be further added is a) 20 litres. b) 30 litres c) 40 litres d) 60 litres.
=
Wednesday, May 3, 2023 C.S.VEERARAGAVAN, APTITUDE TRAINER,[email protected] 15
x ad bcc a b
• 11. A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
• Old ratio 3:5 new ratio 1:1• Qty of water to be added =
11
1. A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3:5.• Let the cost of 1 litre milk be Re. 1• Milk in 1 litre mix. in 1st can =• Milk in 1 litre mix. in 2nd can =• Milk in 1 litre of final mix. =
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First Mean Price
Second type
Ratio of two mixtures =
quantity of mixture taken from each can =12X= 6 litres.
• 1. A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3:5.
• Let the cost of 1 litre milk be Re. 1• Milk in 1 litre mix. in 1st can =.C.P. of 1 litre mix. in 1st can Re. .• Milk in 1 litre mix. in 2nd can = C.P. of 1 litre mix. in 2nd can Re. • Milk in 1 litre of final mix. =. Mean Price = .
First type Mean Price Second type
Ratio of two mixtures = 1:1So, quantity of mixture taken from each can = 6 litres.
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