Discount Questions for Competitive Exams Discount problems with solutions pdf

🚀 Discount: Important Formulas & Shortcuts

• Successive Discount: $D = x + y - \frac{xy}{100}$
• MP and CP Relation: $\frac{MP}{CP} = \frac{100 + P\%}{100 - D\%}$
• Discount Amount: $MP - SP$
• Discount %: $\frac{Discount}{MP} \times 100$

Model 1: Successive Discount

Find the single equivalent discount for two successive discounts of 20% and 10%.

A) 30%

B) 28%

C) 25%

D) 32%

Shortcut: $20 + 10 - \frac{200}{100} = 30 - 2 = 28\%$.

Model 2: Buy X Get Y Free

A shopkeeper offers "Buy 5 Get 3 Free". What is the effective discount percentage?

A) 60%

B) 37.5%

C) 30%

D) 40%

Formula: $\frac{Free}{Total} \times 100 = \frac{3}{8} \times 100 = 37.5\%$.

Model 3: MP/CP Markup

At what % above CP must a trader mark goods to gain 20% after allowing a 10% discount?

A) 33.33%

B) 30%

C) 25%

D) 40%

$\frac{MP}{CP} = \frac{100+20}{100-10} = \frac{120}{90} = \frac{4}{3}$. Markup = 1 on 3 = 33.33%.

Model 4: Profit with Successive Disc.

Goods are marked 50% above CP. If two successive discounts of 10% each are given, find the profit %.

A) 30%

B) 21.5%

C) 25%

D) 20%

Let CP=100, MP=150. Disc = 10% on 150 = 135; then 10% on 135 = 121.5. Profit = 21.5%.

Model 5: Triple Successive

Find the single equivalent discount for 10%, 20% and 25%.

A) 46%

B) 55%

C) 50%

D) 44%

$100 \times 0.9 \times 0.8 \times 0.75 = 54$. Discount = $100 - 54 = 46\%$.

Model 6: Finding MP

After a 15% discount, a watch is sold for ₹1020. What is the Marked Price?

A) ₹1200

B) ₹1180

C) ₹1250

D) ₹1150

$MP = \frac{1020}{85} \times 100 = 12 \times 100 = 1200$.

Model 7: Buy 3 Get 2 + Extra 10%

"Buy 3 Get 2 Free" plus an extra 10% discount. Find total effective discount.

A) 46%

B) 50%

C) 40%

D) 44%

Free items = 40%. Successive of 40% and 10% = $40+10-4 = 46\%$.

Model 8: Markup & Loss

A man marks goods 20% above CP but allows a 30% discount. Find his net loss %.

A) 10%

B) 16%

C) 12%

D) 14%

Let CP=100, MP=120. SP = 70% of 120 = 84. Loss = 16%.

Model 9: Equal Successive Rate

An item of ₹2000 is sold for ₹1620 after two equal successive discounts. Find the rate.

A) 10%

B) 12%

C) 15%

D) 9%

$\frac{1620}{2000} = 0.81$. $\sqrt{0.81} = 0.9$. So discount is 10%.

Model 10: Comparison

Which is better for the buyer: (i) 40% flat or (ii) 20%, 20% successive?

A) Scheme (i)

B) Scheme (ii)

C) Both equal

D) Cannot say

Flat 40% is better. Successive 20%, 20% is only 36%.

Model 11: Finding CP

MP is ₹1600. After 10% discount, profit is 20%. Find CP.

A) ₹1200

B) ₹1300

C) ₹1150

D) ₹1250

$\frac{1600}{CP} = \frac{120}{90} = \frac{4}{3}$. $4CP = 4800 \implies CP = 1200$.

Model 12: Successive Missing Rate

MP is ₹500. Two discounts are given, first is 20%. If final SP is ₹360, find the second rate.

A) 10%

B) 15%

C) 12%

D) 8%

After 20%: $500 - 100 = 400$. To reach 360, need 40 discount on 400 = 10%.

Model 13: Cash Discount

MP of a cycle is ₹5000. Shopkeeper gives 10% discount and additional 5% for cash. Final price?

A) ₹4275

B) ₹4300

C) ₹4250

D) ₹4350

$5000 \times 0.9 \times 0.95 = 4500 \times 0.95 = 4275$.

Model 14: Difference between Discounts

Difference between a flat 30% disc. and two successive 20%, 10% on ₹1000 is:

A) ₹10

B) ₹20

C) ₹30

D) Zero

20%, 10% successive = 28%. Difference = 30% - 28% = 2%. 2% of 1000 = 20.

Model 15: Marked Price vs Selling Price

A man buys at 20% discount on MP and sells at 20% more than MP. Find profit %.

A) 50%

B) 40%

C) 60%

D) 44%

Let MP=100. Buy=80, Sell=120. Profit = 40 on 80 = 50%.

By Wisdom Helps Mahesh Sir | Visit wisdomhelps.in for more