

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 :
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 :

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?

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?

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?
Answers :
1 = 23%, 2 = 9%, 3 = 77%



