Problem Solving

X sold his bicycle at a loss of 9%. if he sold it for 75 more, he would have made a profit of 16%. Find the cost of the cycle.

The way author solved the question is let CP be 100 and SP1=91. To get 16% profit SP2 shuld be 116. so 116-91 = 25.
So if CP is 100 when SP2-SP1=25; What will be CP if SP2-SP1=75 which will be thrice of current CP (300).

But the help I need is related to fundas .. when ever I read such problems I see an ambiguity in the problem. Here first I dont understand the point, "if he sold it for 75 more" - 75 more on what? on the CP or on SP1(91%CP)? when I solved the problem assuming both the scenarios the answers were different. It would be greatly helpful if some on can throw light.. but really sorry for taking your time on silly issue ..

sgarnepudi wrote:X sold his bicycle at a loss of 9%. if he sold it for 75 more, he would have made a profit of 16%. Find the cost of the cycle.

The way author solved the question is let CP be 100 and SP1=91. To get 16% profit SP2 shuld be 116. so 116-91 = 25.
So if CP is 100 when SP2-SP1=25; What will be CP if SP2-SP1=75 which will be thrice of current CP (300).

But the help I need is related to fundas .. when ever I read such problems I see an ambiguity in the problem. Here first I dont understand the point, "if he sold it for 75 more" - 75 more on what? on the CP or on SP1(91%CP)? when I solved the problem assuming both the scenarios the answers were different. It would be greatly helpful if some on can throw light.. but really sorry for taking your time on silly issue ..

First of all no ISSUE is silly. We are all here to learn. And at the end those silly mistakes cost too much on the G-day!


X sold his bicycle at a loss of 9%. if he sold it for 75 more, he would have made a profit of 16%. Find the cost of the cycle.

COST = 100X

100 is a magic number in your calculations!

X sold his bicycle at a loss of 9%. MEANS He sold it for 91X

16 % profit MEANS 116X

and we know from the stem that the difference between his loss, 91X, and his profite, 116X, is 75

75 = 116X - 91X

75 = 25X

X = 3

If you remember, we defined the COST as 100X, so 100x3=300

Master this approach, and you will be fine!

Good luck my friend.

X sold his bicycle at a loss of 9%. if he sold it for 75 more, he would have made a profit of 16%. Find the cost of the cycle.

Let x be the cost of the cycle.

Sold it at a loss of 9% means the sale proce is 91/100*x = .91x

So you would add 75 to this .91x to get a profit of 16% i.e x+16/100*x = 1.16x

Eqn becomes .91x+75 = 1.16x
x=300

Thanks frnds .. I understood the mistake I was doing ..

Ya not different from wat ramya and logitech ! i cant think of nethign else

But a small note ! percentages ! always and always start with number 100 !
trist me as logitech mentioned it works !!

Vishu

I agree 1oo always works and is the best method.

Here is a simpler approach for thsi Qn

9% loss -> 16% profit = 25% change
25% is 75
total shall be

75*4 ie 300

Hope this helps!!