Given number of pair of black socks =4
Let the number of pair of blue socks be x
Let the price of the blue socks per pair be Rs.y
∴ The price of the black socks per pair be Rs.2y
⇒ The original bill =(4×2y+x×y)=8y+xy
⇒ The new bill after interchanged =(4×y+x×2y)=4y+2xy
The new bill is 50% more than the original bill.
∴ (8y+xy)+(8y+xy)×50100=4y+2xy
⇒ (8y+xy)+(8y+xy)2=4y+2xy
⇒ 32×(8y+xy)=4y+2xy
⇒ 32(8+x)=4+2x [ Dividing both sides by y ]
⇒ 3(8+x)=2(4+2x)
⇒ 24+3x=8+4x
⇒ 4x−3x=24−8
⇒ x=16
∴ The number of blue socks in the original bill are 16
⇒ The required ratio =416=14