Question

5. During every financial year, the value of a
machine depreciates by 12%. Find the original
cost of a machine which depreciates by
₹ 2,640 during the second financial year of its
purchase.​

Answer 1

Step-by-step explanation:

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Answer 2

AnsweR :

Rs.25000.

$\bf{\green{\underline{\underline{\bf{Given\::}}}}}$

During every financial year, the value of a machine depreciates by 12%.

Depreciates by Rs.2640 during second financial year of it's purchase.

$\bf{\red{\underline{\underline{\bf{To\:finD\::}}}}}$

The Original cost of a machine.

$\bf{\purple{\underline{\underline{\bf{Explanation\::}}}}}$

Let the original cost of machine be Rs.100.

We know that formula of Simple Interest :

$\bf{\large{\boxed{\sf{Simple\:Interest\:(S.I)=\frac{P\times R\times T}{100} }}}}}}$

$\bf{\orange{\underline{\underline{\bf{\star{For\:1st\:year\::}}}}}}$

$\bf{We\:have}\begin{cases}\sf{Principal,[P]=Rs.100}\\ \sf{Rate,[R]=12\%}\\ \sf{Time,[T]=1\:years}\end{cases}}$

A/q

$\hookrightarrow\tt{Depreciation_{1st}\:=\:\dfrac{100\times 12\times 1}{100} }\\\\\\\\\hookrightarrow\tt{Depreciation_{1st}\:=\:\cancel{\dfrac{1200}{100} }}\\\\\\\\\hookrightarrow\tt{\red{Depreciation_{1st}\:=\:Rs.12}}$

∴ The cost of the end of 1st year = Rs.(100 - 12) = Rs.88.

$\bf{\orange{\underline{\underline{\bf{\star{For\:2nd\:year\::}}}}}}$

$\bf{We\:have}\begin{cases}\sf{Principal,[P]=Rs.88}\\ \sf{Rate,[R]=12\%}\\ \sf{Time,[T]=1\:years}\end{cases}}$

$\hookrightarrow\tt{Depreciation_{2nd}\:=\:\dfrac{88\times 12\times 1}{100} }\\\\\\\\\hookrightarrow\tt{Depreciation_{2nd}\:=\:\cancel{\dfrac{1056}{100} }}\\\\\\\\\hookrightarrow\tt{\red{Depreciation_{2nd}\:=\:Rs.10.56}}$

∴ When depreciation 2nd year is Rs.10.56.

Now,

When depreciation in 2nd year is Rs.2640 with original cost, we get;

$\hookrightarrow\sf{Cost\:of\:Machine=\dfrac{100}{10.56} \times 2640}\\\\\\\\\hookrightarrow\sf{Cost\:of\:machine=\dfrac{100*100}{\cancel{1056}} *\cancel{2640}}\\\\\\\\\hookrightarrow\sf{Cost\:of\:machine=Rs.(100*100*2.5)}\\\\\\\\\hookrightarrow\sf{\red{Cost\:of\:machine=Rs.25000}}$

∴ ThE cosT of thE machiNE is Rs.25000.