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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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