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 Alligation or Mixture :-
 ::Important Formulas ::Examples

Direct Formula / Rule 26 :

• Theorem: Weights of two friends A and B are in the ratio of a : b. A's weight increases by x% and the total weight of A and B together becomes w kg, with an increase of y%.  Then the weight of A = [ a X 100 X w ] kg. (a + b)(100 + y)
 Weight of B = [ b X 100 X w ] kg. (a + b)(100 + y)
 Total weight = Weight of A + Weight of B = [ 100w ] kg. 100 + y
 and the per cent by which weight of B increases = [ y(a + b)-ax ] %. b

• Example :

• Weights of two friends Ram and Shyam are in the ratio of 4 : 5. Ram's weight increases by 10% and the total weight of Ram and Shyam together becomes 82.8 kg, with an increase of 15%. By what percent did the weight of Shyam increase?

• Detail Method :
Let the weights of Ram and Shyarn be 4x and 5x.
Now, according to question,  = 4x X 100 + Shyam's new wt = 82.8...(i) 100
 = (4x + 5x) = 9x X 115 = 82.8...(i) 100 100
From (ii), x = 8 Putting in (i), we get Shyam's new wt = (82.8 - 35.2) = 47.6  % increase in Shyam's wt= (47.6 - 40) X 100 = 19% 40

• Ailigation Method :
 Ram Shyam
 10% 15% x% 4 5 (given)
 = x - 15 = 4 15 - 10 5
or, x - 15 = 4 ∴ x = 19

• Quicker Method : Here you can use direct formula :
% increase in Shyam's weight  = 15 X 9 - 4 X 10 = 95 = 19%. 5 5

Exercise :
1. Weights of two friends Naval and Keval are in the ratio of 3 : 4. Naval's weight increases by 16% and the total weight of Naval and Keval together becomes 83 kg, with an increase of 20%. By what per cent did the weight of Keval increase?
2. Weights of two friends Pran and Prem are in the ratio of 2 : 3. Pran's weight increases by 6 1/2% and the total weight of Pran and Prem together becomes 41 kg, with an increase of 8%. By what per cent did the weight of Prem increase?
3. Weights of two friends Sudhir and Sudhesh are in the ratio of 4 : 1. Sudhir's weight increases by 12% and the total weight of Sudhir and Sudhesh together becomes 50 kg, with an increase of 25%. By what per cent did the weight of Sudhesh increase?
4. Answers : 1 = 23%,   2 = 9%,   3 = 77%