Profit, Loss & Discount · Topic 3 of 8

🔻 Successive Discounts

2 exam question types, fully solved

Two discounts one after another are never their sum — the second comes off the already-reduced price, so the real discount is always less than a + b.

The single equivalent discount

Two discounts a% and b% equal a single discount of a + b − %. So 20% and 10% give 30 − 2 = 28%, never 30%.

• Or multiply the surviving fractions: is the part still paid; 1 minus it is the discount.

• For three discounts, combine two into one equivalent, then combine with the third — or chain the fractions once: 25%, 20% and 10% leave paid, a single 46% discount (tag ₹600 → pay ₹324).

• “Buy n, get m free” is a discount of : buy 3 get 1 free → = 25% off, never 33%.

Slabs & conditions: for “X% off above ₹N”, use only the single highest slab reached — they don't stack. And “>₹N” excludes the exact value ₹N.

🏷️Discount CalculatorDiscount is on MP

first discount %

second discount %

Single equivalent = a + b − ab/100 = 20 + 10 − (20×10)/100

= 28% off (not 30%)

Discounts of 20% and 10% equal a single discount of 30 − 2 = %.

Q1Two successive discounts of 10% and 20% equal a single discount of:

Q2On MP ₹500, discounts of 20% then 10% give SP:

Q3Two equal discounts giving a single 19% discount means each is:

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Real exam questions — Successive Discounts

2 question types · 6 solved examples from real SSC papers

Two discounts in a row are never their sum — the second comes off the reduced price. Use the single equivalent.

How to solve this type

Two successive discounts of a% and b% are never a+b. The fast way: a single equivalent discount of

a+b-\dfrac{ab}{100}

%. Equivalently, multiply the two surviving fractions

\dfrac{100-a}{100}\times\dfrac{100-b}{100}

— that gives the fraction of the price the customer still pays, and 1 minus it is the discount. For three discounts, combine the first two into one equivalent, then combine that with the third. To find an original/marked price, multiply all the surviving fractions and divide the amount paid by that product. Because the answer is always below a+b, you can instantly reject any option ≥ a+b.

Two successive discounts of 20% and 10% are equal to a single discount of:

A28%B29%C30%D32%

A shirt has 25% off, plus 20% for cash, plus 10% for a loyal customer. She paid ₹324. The price tag was (in ₹):

A600B650C725D750

On a bill, the difference between a single 27% discount and two successive discounts of 20% and 10% was ₹56. The bill amount was:

A₹1,120B₹1,866C₹5,500D₹5,600