UPSC Civil Services 2015 Prelims General Studies Paper II

Let number of a pairs of brown socks = y
Price of brown socks = x
Price of black socks = 3x
According to question
⇒ 5 × 3x + yx = 100 ... (i)
Now, clerk has interchanged socks pairs then price is increased by 100%
3xy+5x=(15x+yx) +

(15x+yx)×100

100

= 3xy + 5x = 30x + 2xy ... (ii)
⇒ 30x + 2yx = 3xy + 5x
⇒ 25x = xy
y = 25
∴ So, number of brown socks = 25