Bunuel wrote:

The price of a shirt was first discounted by a certain percent and later by 25 percent of the discounted price. If these two discounts are equivalent to a single discount of 40 percent of the original price, what was the first discount?

A. 10%

B. 15%

C. 20%

D. 30%

E. 65%

Method 2:

The second method is similar to the first one, but instead of using a formula, we will solve it by assuming the original price to P and applying the discounts on it.

Original Price : P

Price after first discount \(= P ( 1 - \frac{F}{100})\) , where F is the first discount.

Price after the second discount \(= P ( 1 - \frac{F}{100}) ( 1 - \frac{25}{100}) = \frac{3P}{4} * ( 1 - \frac{F}{100})\) ......(i)

According to the question stem, the two successive discount is equivalent to one discount of 40%.

Thus, price after overall discount can be written as \(P ( 1 - \frac{40}{100}) = \frac{3P}{5}\) ........(ii)

Equating equation (i) and (ii), we will get

\(\frac{3P}{4} * (1 - \frac{F}{100}) = \frac{3P}{5}\)

\(5 - \frac{5F}{100} = 4\)

\(\frac{F}{20} = 1\)

\(F = 20\)%

Thus, the correct answer is

Option C.

_________________

Register for free sessions

Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions

Quant Workshop:- Get 100 practice questions | Free Strategy Weession:- Key strategy to score 760

Success Stories

Q38 to Q50 | Q35 to Q50 | More Success Stories

Ace GMAT

Articles and Question to reach Q51 | Question of the week | Tips From V40+ Scoreres | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Must Read Articles

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2

Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2

Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability

Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry

Algebra- Wavy line | Inequalities

Practice Questions

Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com