The cost price and selling price of rice are the same. Due to a faulty weighing machine, the seller earns a 15% profit. If Rs. x is the cost price of 1000 gm rice and the machine is changed which shows 1000 gm instead of 950 gm, what should be the selling price (in Rs.) now to get the same percentage of profit?

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SSC CGL 2023 Tier-I Official Paper (Held On: 20 Jul 2023 Shift 4)
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  1. 1.0295x
  2. 1.0259x
  3. 1.0925x
  4. 1.0950x

Answer (Detailed Solution Below)

Option 3 : 1.0925x
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SSC CGL Tier 1 2025 Full Test - 01
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Detailed Solution

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Concept used:

1 Kilogram = 1000 gm

Formula used

Gain = Selling Price - Cost Price

Gain% = (S.P - C.P)/C.P × 100(������� ����� − ���� �����)���������×100%(������� ����� − ���� �����)���������×100%(������� ����� − ���� �����)���������×100% <math xmlns="/"><mrow data-mjx-texclass="ORD"><mfrac><mrow><mo stretchy="false">(<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mtext> <mi>�<mi>�<mi>�<mi>�<mi>�<mtext> <mo>−<mtext> <mi>�<mi>�<mi>�<mi>�<mtext> <mi>�<mi>�<mi>�<mi>�<mi>�<mo stretchy="false">)<mrow><mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mo>×<mn>100<mi mathvariant="normal">% <math xmlns="/"><mrow data-mjx-texclass="ORD"><mfrac><mrow><mo stretchy="false">(<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mtext> <mi>�<mi>�<mi>�<mi>�<mi>�<mtext> <mo>−<mtext> <mi>�<mi>�<mi>�<mi>�<mtext> <mi>�<mi>�<mi>�<mi>�<mi>�<mo stretchy="false">)<mrow><mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mo>×<mn>100<mi mathvariant="normal">% <math xmlns="/"><mrow data-mjx-texclass="ORD"><mfrac><mrow><mo stretchy="false">(<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mtext> <mi>�<mi>�<mi>�<mi>�<mi>�<mtext> <mo>−<mtext> <mi>�<mi>�<mi>�<mi>�<mtext> <mi>�<mi>�<mi>�<mi>�<mi>�<mo stretchy="false">)<mrow><mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mo>×<mn>100<mi mathvariant="normal">% <math xmlns="/"><mrow data-mjx-texclass="ORD"><mfrac><mrow><mo stretchy="false">(<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mtext> <mi>�<mi>�<mi>�<mi>�<mi>�<mtext> <mo>−<mtext> <mi>�<mi>�<mi>�<mi>�<mtext> <mi>�<mi>�<mi>�<mi>�<mi>�<mo stretchy="false">)<mrow><mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mi>�<mo>×<mn>100<mi mathvariant="normal">%

Calculation: 

The cost price of 1000 gm rice is x.

The cost price of 950gm rice = x/1000 × 950 = Rs. 95x/100

To earn a profit of 15% after the faulty weight, the S.P should be:

⇒ 95x/100 × 115/100

⇒ 10925x/10000

⇒ 1.0925x

The answer is 1.0925x.

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