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1) In what ratio must onion at Rs.30/kg combined with onion at Rs.10.80/kg so that the combination of worth Rs.10per kg is?
If 2 substances are combined, then the needed ratio is given by, the rule of allegation
C.P of a unit quantity of cheaper (c) C.P. of a unit quantity of dearer (d)
Mean Onion Price (m)
d-m m-c
Therefore, needed ratio is cheaper quantity : dearer quantity = (d-m) : (m-c)
Answer: 8:7
By the rule of allegation
i. C.P of 1 Kg of onion of I kind(p) = 930
ii. C.P of 1 Kg of onion of II kind (p)= 1080
iii. Mean onion (p) = 1000
iv. d – m = 1080-1000 = 80
v. m – c = 1000 – 930 = 70
Therefore, needed = 80 : 70 = 8 : 7
2. what is ratio must in rice at Rs.3.20/KG be combined with rice at Rs.2.90/kg so that the combination of worth Rs.3.08/kg is,
If 2 substances are combined, then the needed ratio is given by, the rule of allegation
Required ratio is cheaper quantity : dearer quantity = (d-m) : (m-c)
Answer : 3:2
Given
i. C.P of a kg quantity of I kind (p) = 3.20
ii. C.P of a kg quantity of II kind (p) = 2.90
iii. Mean rice price (p) = 3.08
iv. d – m = 3.08 – 2.90 = 0.18
v. m – c = 3.20 – 3.08 = 0.12
Therefore, Needed ratio = 0.18 : 0.12 = 3 : 2
3. How many kg’s of salt pricing Rs.9/per kg must be combined with 27 kg of salt pricing Rs.7/kg so that 3 may be obtain of 10% by selling the combination at Rs.9.24/kg?
i. If Salt Price and obtain are given, C.Price=[ (100 / (100+gain%)xS.P ] Rs.
ii. From the rule of allegation
Answer : 63 KG
Step I : Salt Price of 1 kg of combination= Rs. 9.24
obtain= 10%
C.P of 1 kg of combination =[ (100) / (100+10)x9.24 ] = Rs. 8.40
Salts price = Rs. 8.40/-
Step (ii) By the rule of allegation
vi. C.P of 1 kg of salt of I kind (p) = 900
vii. C.P of 1 kg of salt of II kind (p) = 700
viii. Mean salt price (p) = 840
ix. d – m = 900 - 840 = 60
x. m – c = 840 – 700 = 140
Needed ratio = 140 : 60 = 7 : 3
Step (iii) Let (x) kg of salt of I kind be combined with 27 kg of II kind
7 : 3 = x : 27 => 7/3 = (x/27) => x = (7/3)*(27)= 63 kg.
4. What is the ratio of water must be combined with coffee to obtain 16 (2/3)% on marketing the combinations price is?
iii. If S.P and gain are given, C.P = [ (100) / (100+gain%)xS.P ] Rs.
iv. The rule of allegation
Required ratio is cheaper quantity : dearer quantity = (d-m) : (m-c)
Answer = 1 : 6
i) Let C.P of 1 cup of coffee be Rs.1
And S.P of1 cup of coffee be Rs.1
Gain = 50/3%
C.P of 1 cup of combination =[ (100) / (100+5/3)x1 ]
= Re. 100 x 3/350 x 1 = 6/7 (Mean price)
ii) By the rule of allegation
I. C.P of 1 cup of water = 0
II. C.P of 1 cup of coffee = 1
III. Mean price (p) = 6/7
IV. d – m = 1 – 6/7 = 1/7
V. m – c = 6/7 - 0 = 6/7
Therefore, ratio of water and coffee = 1/7 : 6/7 = 1 : 6
5. Two cups X and Y contain coffee and water combined in the ratio 8:5 and 5:2 correspondingly. What is the ratio in these 2 combinations be combined to get a new combination has coffee and a water in the ratio of 9:4?
Rule of allegation
Answer = 2:7
i) : If C.P. of coffee be Re.1
Given ratio of combination in X= 8:5
Coffee in 1 cup combination in X = (8/13)cups
C.P of 1 cup combination in X= Rs. 8/13
Therefore, The ratio of Combination in Y = 5:2
Coffee in 1 cup combination in Y – (5/7) cups
C.P of 1 cup combination in B = Rs. 5/7
Ratio of new combination = 9:4
milk in 1 cup combination = 9/13
C.P of 1 cup combination = Rs/ 9/13 (Mean price)
ii) : By the rule of allegation,
i. C.P of 1 cup of combination in X =8/13
ii. C.P of 1 cup of combination in Y = 5/7
iii. Mean price (p) = 9/13
iv. d – m = 9/13 – 5-7 = 2/91
v. m – c = 9/13 – 8/13 = 1/13
Needed ratio = 2/91 : 1/13 = 2:7
6. In what ratio Coffee be combined with water pricing Rs.12 /cup to gain a combination worth of Rs.8 / cup?
Rule of Allegation
Answer = 1 : 2
By the rule of allegation,
i. C.P of 1 cup of water = 0
ii. C.P of 1 liter of coffee = 12
iii. Mean price (p) = 8
iv. d – m = 12-8 = 4
v. m – c = 8-0 = 8
Ratio of water and coffee = 4 : 8 = 1 : 2
7. Addition of Rs.4000 is given out in 2 pieces, one at 8% S.I and the other at 10% S. I. In the annual interest is Rs.352, the addition is given at 8% is
S.I = PNR / 100
Answer = Rs. 2400
i) Given the total sum = Rs. 4000
If the sum given at 8% be Rs.a
ie) P = a , n=1, R = 8%
(aX18/100) = (8a/100)
If the addition given at 10% be Rs. 4000 – a
P = 4000-a , n=1, R = 10%
(4000 - aX1X10)/(100) = (40000-10a)/100
Given Annual interest is Rs. 352
(8a/100) + (40000-10a)/100 = 352
8a – 10a = 35200 – 40000
-2a = -4800
X = (4800/2)= Rs.2400/-
8. A supplier has 1000 kg of salt, part of which he/she sells at 8% revenue and the rest at 18% revenue. He/she obtains 14% on the overall. The amount offered at 18% revenue is
Rule of Allegation
Answer = 600 kg
Revenue on I kind (%) (c) Revenue of II kind (d)
8 18
Mean Price (m)
d-m (18-14) = 4 14 m-c (14-8) = 6
Ratio of revenues on I and II = 4:6 = 2:3
ii) Amount offered at 18% revenue = (3/5 x 1000) kg
= 600 kg.
9. 2 jars X and Y has Horlicks and water mixed in the ratio of 4:3 and 2:3, in what ratio must these combinations be combined to create a new combination containing half Horlicks and half water?
Ans: 7:5
Rule of Allegation
Answer = 7 : 5
i): Let C.P. of 1 spoon Horlicks = Re.1
Ratio of Combination in X = 4:3
Horlicks in 1 spoon combination in X = 4/7 spoons,
Therefore, C.P of 1 spoon combination of X = Rs. 4/7
Ratio of combination in Y = 2:3
Horlicks in 1 litre combination in Y = 2/5 litre,
Therefore, C.P of 1 litre combination of Y = Rs. 2/5
Ratio of new combination = 1:1
Horlicks in 1 litre combination = (1/2) litre,
Therefore, C.P of 1 litre combination = Rs.(½ )
(Mean price = Rs.( ½ )
ii) By the rule of alligation
Needed Ratio = 1/14 : 1/10 = 7 : 5
10. A vessel is full of Coconut drink has 40% sugar. A part of this Coconut drink is replaced by another one has 19% sugar and now the percentage of Coconut drink was found to be 26% amount of Coconut drink replaced is
Rule of Allegation
Answer (2/3)
i) :By the rule of Allegation
Ratio of I and II kind = 7: 14 = 1:2
ii) : Amount of Coconut drink replaced in II kind = 2/3
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