Pretty Pink Bonnet

[ajith]

My brother, Chris, is a little simple. I recently asked him to buy me some ribbon for my daughter's pretty bonnet. He went to the haberdashery shop for the required length but accidentally interchanged the feet and inches. When I measured the resulting ribbon I only had 5/8 of the length I required. How much ribbon did I originally ask for?

a) 66 inches

b) 77 inches

c) 88 inches

d) 176 inches

e) 55 inches

[spoiler]OA :C[/spoiler]

[harsh.champ]

My brother, Chris, is a little simple. I recently asked him to buy me some ribbon for my daughter's pretty bonnet. He went to the haberdashery shop for the required length but accidentally interchanged the feet and inches. When I measured the resulting ribbon I only had 5/8 of the length I required. How much ribbon did I originally ask for?

a) 66 inches = 5ft 6inches

b) 77 inches = 6feet 5 inches

c) 88 inches = 7feet 4inches

d) 176 inches = 14feet 8inches

e) 55 inches

= 4feet 7inches

Woah!A question posted by ajith.Now this is rare to find.
Let me give a try if I can solve it .
Let it be a feet and b inches
Total = 12 x a + b
=12a + b
Now Chris bought 12b + a

12b + a = 5/8(12a + b)
52a = 91b
So a = 91/52 b =7/4b
or 4a =7b
or 4 x (no. of feet) = 7(no. of inches)

Checking the option choices,I find C.

The trap is b/w C and E i suppose.

[kstv]

IMO C.
But the method I use was not elegant.
Ribbon I ordered is 12x + y, but got 12y + x
12x+y/12y+x = 5/8
using componendo / divinendo

11(x-y)/13(x+y) = 3/13
11(x-y) = 3(x+y)

so x-y = 3 and x+y = 11

It is easier to compare the answers.

[anki_jain]

original lenth would be 8/5x.

check with options:

8/5x=88 => x=55
i.e. 33 short or 3/8 short from original length. IMO C

[kstv]

sorry I have been chastened by ajith for not rechecking.
I edited my post.