Shelf A has 4/5 of the number of books that shelf B has. If 25% of the

1.	Shelf A has 4/5 of the number of books that shelf B has. If 25% of the books in A are transferred to B and then 25% of the books from B are transferred to A, then the percentage of the total number of books that A will have is1). 252). 503). 754). 100
Answer» LET the total number of books shelf A GOT be X. According to data- Shelf A has 4/5 of the number of books that shelf B has ⇒ number of books on shelf B = 5x/4 As 25% of books of shelf A are transferred to shelf B. New numbers of books on shelf B = number of books initially on shelf B + number of transferred books ⇒ New numbers of books on shelf B = (5x/4) + (25x/100) ⇒ New numbers of books shelf B got = 1.5x At the same TIME, Number of books on shelf A = x – (25x/100) = 0.75x Then 25% of books from shelf B are been transferred to shelf A ∴ New number of books on shelf A = number of books shelf A after first transfer + number of books transferred from shelf B to shelf A ∴ New number of books on shelf A = 0.75x + (25 % of 1.5x) = 1.125x New number of books on shelf B = Number of books on shelf B after first transfer – number of books transferred from shelf B to shelf A New number of books on shelf B = 1.5x – (25 % of 1.5x) = 1.125x ⇒ The PERCENTAGE of the total number of books on shelf A = $(\frac{{1.125x}}{{1.125x + 1.125x}} \times 100 = 50)$

Shelf A has 4/5 of the number of books that shelf B has. If 25% of the books in A are transferred to B and then 25% of the books from B are transferred to A, then the percentage of the total number of books that A will have is1). 252). 503). 754). 100

Answer»

LET the total number of books shelf A GOT be X.

According to data-

Shelf A has 4/5 of the number of books that shelf B has

⇒ number of books on shelf B = 5x/4

As 25% of books of shelf A are transferred to shelf B.

New numbers of books on shelf B = number of books initially on shelf B + number of transferred books

⇒ New numbers of books on shelf B = (5x/4) + (25x/100)

⇒ New numbers of books shelf B got = 1.5x

At the same TIME, Number of books on shelf A = x – (25x/100) = 0.75x

Then 25% of books from shelf B are been transferred to shelf A

∴ New number of books on shelf A = number of books shelf A after first transfer + number of books transferred from shelf B to shelf A

∴ New number of books on shelf A = 0.75x + (25 % of 1.5x) = 1.125x

New number of books on shelf B = Number of books on shelf B after first transfer – number of books transferred from shelf B to shelf A

New number of books on shelf B = 1.5x – (25 % of 1.5x) = 1.125x

⇒ The PERCENTAGE of the total number of books on shelf A = $(\frac{{1.125x}}{{1.125x + 1.125x}} \times 100 = 50)$