Shortcut:
The quantity of salt at Rs 'a' per kg that a man must mix with 'm' kg of salt at Rs 'b' per kg, so that he may, on selling the mixture at Rs 'c' per kg, gain 'g%' on the outlay is given by
100c − b(100 + g)
/
a(100 + g) − 100c
x m
Note: If we suppose that the quantity of salt at Rs a per kg is n, then
n =
100c − b(100 + g)
/
a(100 + g) − 100c
x m
Here, a = 16.50, b = 24.5, c = ?, g = 25, n = 25, m = 35
Using these values in the shortcut, we get:
25 =
100 x c − 24.50(100 + 25)
/
16.50(100 + 25) − 100 x c
x 35
25 =
100c − 24.50 x 125
/
16.50 x 125 − 100c
x 35
25 =
100c − 3062.5
/
2062.5 − 100c
x 35
25(2062.5 − 100c) = (100c − 3062.5)35
5(2062.5 − 100c) = (100c − 3062.5)7
10312.5 − 500c = 700c − 21437.50
1200c = 31750
∴ c =
31750
/
1200
= 26.458 or 26.50
Hence, the should the mixture at Rs 26.50 per kg.
