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QuestionIn a library, 40%40\% of books are in English, 80%80\% of the rest are in Hindi, and 240 are in other languages. Total books?

Studdy Solution

STEP 1

Assumptions1.40% of the total books are in English.80% of the remaining books are in Hindi3. The remaining240 books are in various other regional languages

STEP 2

First, we need to find the number of books that are neither in English nor in Hindi. We know that this number is240.
Let's denote the total number of books as ,thenumberofEnglishbooksas, the number of English books as , the number of Hindi books as HH, and the number of books in other languages as $$.
From the problem, we know that=240 =240

STEP 3

We also know that80% of the remaining books after the English books are removed are in Hindi. So, we can writeH=0.8×(−)H =0.8 \times ( -)

STEP 4

And we know that40% of the total books are in English. So, we can write=0.4× =0.4 \times

STEP 5

The total number of books is the sum of the English books, Hindi books, and other books. So, we can write=+H+O = + H + O

STEP 6

Substitute the expressions for , $H$, and from steps3,4, and2 into the equation from step5.
=0.4+0.8(T−0.4)+240 =0.4 +0.8(T -0.4) +240

STEP 7

implify the equation from step6.
=0.4+0.−0.32+240 =0.4 +0. -0.32 +240

STEP 8

Combine like terms.
=0.88+240 =0.88 +240

STEP 9

Subtract .88.88 from both sides of the equation.
.12=240.12 =240

STEP 10

Divide both sides of the equation by 0.120.12 to solve for $$.
=240/0.12 =240 /0.12

STEP 11

Calculate the total number of books.
=240/0.=2000 =240 /0. =2000The total number of books in the library is2000. So, the correct answer is (d)2000.

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