A shopkeeper cheats to the extent of 12% while buying and selling goods, by using tampered weights. His total gain in percentage is:

## Answer

Correct Answer : d ) 27.27%

Explanation :NOTE: Candidates there is a debate on such questions among different exams like SSC, Railways and CAT. To solve this question, we consider an assumption that promised cost price while selling to the customer is same as the promised cost price while buying the goods from wholesaler. We consider this assumption because it will be practical to say that Fraud can take place on quantity rather than price of a product.

But RRB sometimes consider the assumption that fraud takes place on the cost price rather than quantity. So, if you see both the options i.e. 19.7% (taking fraud on quantity) and 18.81% (taking fraud on price), then chose option with fraud on quantity otherwise chose option with fraud on quantity

Taking Fraud on quantity

**Approach 1:**

As, shopkeeper sold 880 units of goods instead of 1000 units and brought 1120 units of goods instead of 1000 units

So, on sale of 880 units he gains 240 units of goods

Thus,

Loss%=\(Goods \ gain \over Goods \ sold\)*100= \(240 \over 880\)*100=27.27 %

Hence, (d) is the correct answer.

Approach 2:

According to question:

As shopkeeper cheats of 12% at the time of buying

Suppose he wants to buy 1000 units of goods at Rs. 1000

Actual units of goods purchased by shopkeeper=\(1000+(1000*{12\over 100})=1120\)

⇒ Cost price (CP) of 1120 units = Rs. 1000

⇒CP of 1 unit=Rs. \(1000 \over 1120\)

As shopkeeper cheats of 12% at the time of selling

Suppose he promise to sells 1000 units of goods at Rs. 1000

Actual units of goods sold by shopkeeper=\(1000-(1000*{12\over 100})=880\)

⇒ Selling price (SP) of 880 units = Rs. 1000

⇒SP of 1 unit=Rs. \(1000\over 880\)

Thus, the required profit%=\({{SP-CP}\over{CP}}*100\)=\({{{1000\over880}-{1000\over1120}}\over{1000\over1120}}*100\)=27.27%

Hence, (d) is the correct answer.

Taking Fraud on Price

If shopkeeper cheats to the extent of x% while buying and selling then overall profit can be calculated by

Overall profit=\(x\%+x\%+{{x\%*x\%}\over100}\)

⇒Overall profit=\(12+12+{{12*12}\over100}\)=25.44 %

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc.

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