Solutions: Profit, Loss & Discount - Vardaan Learning Institute

1. A man sold a fan for ₹465. Find the cost price if he incurred a loss of $7\%$.

Solution:
$SP = ₹465$, Loss% = $7\%$.
$SP = CP \times (1 - \frac{Loss}{100})$
$465 = CP \times \frac{93}{100} \Rightarrow CP = \frac{465 \times 100}{93} = 500$.
Cost Price = ₹500.

2. If the manufacturer gains $10\%$, the wholesale dealer $15\%$ and the retailer $25\%$, then find the cost of production...

Solution:
Let Prod Cost = $x$.
Price after manuf = $x \times 1.1$
Price after whole = $x \times 1.1 \times 1.15$
Final Retail = $x \times 1.1 \times 1.15 \times 1.25 = 1265$
$1.58125x = 1265 \Rightarrow x = 800$.
Cost = ₹800.

3. A shopkeeper marks his goods... discount $25\%$... profit $50\%$. Find ratio CP:MP.

Solution:
$SP = MP \times 0.75$.
$SP = CP \times 1.5$.
$\Rightarrow 0.75 MP = 1.5 CP \Rightarrow \frac{CP}{MP} = \frac{0.75}{1.5} = \frac{1}{2}$.
Ratio is 1:2.

4. A bag is marked at ₹80. It is sold for ₹68. The rate of discount is?

Solution:
Discount = $80 - 68 = 12$.
Rate = $\frac{12}{80} \times 100 = 15\%$.

5. By selling 33 m of cloth, a shopkeeper gains the selling price of 11 m of cloth. Find his gain per cent.

Solution:
Gain = SP of 11m.
Gain = SP - CP $\Rightarrow$ SP(11) = SP(33) - CP(33)
$\Rightarrow CP(33) = SP(33) - SP(11) = SP(22)$.
$\text{Gain } \% = \frac{\text{Gain}}{\text{CP of 33}} \times 100 = \frac{SP(11)}{SP(22)} \times 100 = \frac{11}{22} \times 100 = 50\%$.

6. A dealer buys an article marked at ₹25,000 with a discount of $20\%$ and $5\%$ off...

Solution:
Net Price = $25000 \times 0.8 \times 0.95 = 25000 \times 0.76 = 19,000$.
Total CP = $19000 + 1000 = 20,000$.
SP = 25,000.
Gain = 5,000.
Gain% = $\frac{5000}{20000} \times 100 = 25\%$.

7. Two articles are sold for ₹9,900 each. On one $10\%$ gain, other $10\%$ loss.

Solution:
Case 1: $SP=9900$, Gain=10%. $CP = \frac{9900}{1.1} = 9000$.
Case 2: $SP=9900$, Loss=10%. $CP = \frac{9900}{0.9} = 11000$.
Total CP = $20000$. Total SP = $19800$.
Loss = 200.
Loss% = $\frac{200}{20000} \times 100 = 1\%$ Loss.

8. ...sold a cupboard for ₹5,400... dining table for ₹6,300. Discount 10%.

Solution:
$MP = \frac{SP}{0.9}$.
Cupboard MP = $\frac{5400}{0.9} = 6000$.
Dining Table MP = $\frac{6300}{0.9} = 7000$.

9. Waheeda bought an air cooler for ₹3300 including a tax of $10\%$.

Solution:
Let Price before tax = $P$.
$P \times 1.10 = 3300 \Rightarrow P = 3000$.
If tax is 12%, New Price = $3000 \times 1.12 = 3360$.
Extra amt = $3360 - 3300 = ₹60$.

10. A bicycle is sold at a gain of $16\%$...

Solution:
Diff in perc = $20\% - 16\% = 4\%$.
So, $4\%$ of CP = ₹20.
$\frac{4}{100} \times CP = 20 \Rightarrow CP = 500$.

11. A shopkeeper allows $23\%$ commission... gains ₹56 on one item... profit 10%.

Solution:
Gain = ₹56, which is 10% of CP. So CP = 560.
SP = CP + Gain = $560 + 56 = 616$.
$SP = MP \times (1 - 0.23) = MP \times 0.77$.
$0.77 MP = 616 \Rightarrow MP = \frac{616}{0.77} = 800$.
Advertised Price = ₹800.

12. The list price of a frock is ₹220. A discount of $20\%$... second discount $10\%$.

Solution:
1st Discount: $220 \times 0.2 = 44$. Price = $220 - 44 = 176$.
2nd Discount: 10% on 176 = 17.6.
Final SP = $176 - 17.6 = 158.4$.

13. By selling a cricket bat for ₹450, a man loses $10\%$.

Solution:
$SP=450$, Loss=10%. $CP = \frac{450}{0.9} = 500$.
To gain 5%: New SP = $500 \times 1.05 = 525$.

14. A grocer purchased 200 kg of rice at ₹25 per kg...

Solution:
Total CP = $200 \times 25 = 5000$.
Total Target S.P. (8% gain) = $5000 \times 1.08 = 5400$.
S.P. of 80 kg (10% gain) = $80 \times 25 \times 1.1 = 2200$.
S.P. of 40 kg (4% loss) = $40 \times 25 \times 0.96 = 960$.
Remaining amt needed = $5400 - (2200 + 960) = 5400 - 3160 = 2240$.
Remaining qty = $200 - 120 = 80 \text{ kg}$.
Rate = $2240 / 80 = 28$.
Must sell at ₹28 per kg.

15. A trader marks his goods...

Solution:
CP = 85. Profit = 20%. SP = $85 \times 1.2 = 102$.
$SP = MP \times 0.85$.
$102 = MP \times 0.85 \Rightarrow MP = \frac{102}{0.85} = 120$.
Marked Price = ₹120.