A man ordered 4 pairs of red socks and some additional pairs of grey socks. The price of the red socks per pair was twice to that of the grey socks. However when the salesman entered the order it was found that the number of pairs of the two colours had been interchanged which had increased the bill by 25%. Find the ratio of the number of pairs of red socks to the number of pairs of grey socks in the original order.
1:2
Let the price per pair of grey socks = ₹p, so the price per pair of red socks = ₹2p (since red socks cost twice as much as grey).
Let the number of grey pairs originally ordered = g. The man ordered 4 pairs of red socks.
Original bill = (4 pairs of red × 2p) + (g pairs of grey × p) = 8p + gp
When the salesman entered the order, the QUANTITIES of the two colours got interchanged (not the prices): so now the bill is calculated as if he ordered g pairs of red socks and 4 pairs of grey socks.
New bill = (g × 2p) + (4 × p) = 2gp + 4p
It is given that this new bill is 25% more than the original bill:
New bill = 1.25 × Original bill
2gp + 4p = 1.25 × (8p + gp)
2gp + 4p = 10p + 1.25gp
2gp − 1.25gp = 10p − 4p
0.75gp = 6p
0.75g = 6
g = 8
So originally he ordered 4 pairs of red socks and 8 pairs of grey socks.
Ratio of red : grey = 4 : 8 = 1 : 2
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