pairs of black socks and some additional pairs of blue socks. The price of the black socks per pair was twice that of the blue. When the order was filled, it was found that the number of pairs of the two colors had been interchanged. This increased the bill by %. The ratio of the number of the pairs of black socks to the number of pairs of blue socks in the original order can be expressed as in the simplified form. Find .
John ordered
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If the price of each pair of Black socks = x & the number of pairs of blue socks = b,
Then, Correct price of Socks were = 4x + bx/2
And after interchange the price became = 4x/2 + bx
It made the price 1.5 times i.e. 3/2 times higher.
So,
4x/2 + bx = 3/2 (4x + bx/2)
2x + bx = 6x + 3bx/4
(4bx - 3bx)/4 = 6x - 2x
bx = 16x
b = 16.
Then the blue socks were 16 pairs.
So, the ratio = a : b = 4 : 16 = 1 : 4
And a + b = 5.