TIFR CSE 2012 | Part A | Question: 6

Question

A certain pair of used shoes can be repaired for $Rs.1250$ and will last for $1$ year. A pair of the same kind of shoes can be purchased new for $Rs.2800$ and will last for $2$ years. The average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes?

• A. $5%$
• B. $12%$
• C. $15%$
• D. $3%$
• E. $24%$

Answer 1

Repaired shoes lasts $1$ year worth  $Rs. 1250$

New shoes lasts $2$ year worth $Rs. 2800$

So, for one year new shoes costs $Rs. 1400$

% greater of new shoes cost than the cost of repaired shoes  $(1400-1250 / 1250)$ = 12% (option b)

Comments

Can you explain ?
% greater of new shoes cost than the cost of repaired shoes  (1400−1250/1250)(1400−1250/1250) = 12% (option b)

Answer 2

Cost of repairing shoes for 1 year=1250

Cost of purchasing new shoes for 1 year=1400(since 2800 for 2 years)

Let cost per year of the new shoes is x% greater than cost of repairing used shoes.

Then,1400 is x% greater than 1250.

1400=(1+x/100)*1250

Now,1+x/100=1400/1250

1+x/100=1.12

x/100=.12

x=12