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Question

If the expenditures of companies A and B in 2001 were equal and the total income of the two companies was Rs 116 lakhs, what was the total expenditure of the two companies in that year?

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Solution

The correct option is **B** Rs 80 lakhs

Let the income of company A = Rs x lakhs

∴ Income of company B = Rs (116 - x) lakhs

Let the expenditure of each company be Rs y lakhs

For company A,

40=x−yy×100

⇒40y=(x−y)×100

⇒x−y=40y100=2y5

⇒x=2y5+y

=7y5 ...(i)

For company B,

50=(116−x)−yy×100

⇒y=2(116−x)−2y

⇒3y=232−2x

⇒3y=232−2×7y5 [From Eq.(i)]

⇒3y=232−14y5

⇒3y+14y5=232

⇒29y5=232

⇒y=232×529=40

∴ Total Expenditure = 2y

= 2 × 40

= Rs 80 lakhs

Let the income of company A = Rs x lakhs

∴ Income of company B = Rs (116 - x) lakhs

Let the expenditure of each company be Rs y lakhs

For company A,

40=x−yy×100

⇒40y=(x−y)×100

⇒x−y=40y100=2y5

⇒x=2y5+y

=7y5 ...(i)

For company B,

50=(116−x)−yy×100

⇒y=2(116−x)−2y

⇒3y=232−2x

⇒3y=232−2×7y5 [From Eq.(i)]

⇒3y=232−14y5

⇒3y+14y5=232

⇒29y5=232

⇒y=232×529=40

∴ Total Expenditure = 2y

= 2 × 40

= Rs 80 lakhs

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