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21 Apr 2023, 01:30
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Difficulty:
25%
(medium)
Question Stats:
84% (02:13) correct
16%
(02:31)
wrong
based on 82
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A school library consists of literature books and science books in the ratio of 5:6. If 50 more literature books are added to the library and the number of science books is increased by 1/4th of the existing science books, the ratio of the literature books and science books increases to 4:3. If the library consists of only literature and the science books, what is the initial number of books in the library?
A. 60
B. 110
C. 130
D. 140
E. 190
A. 60
B. 110
C. 130
D. 140
E. 190
21 Apr 2023, 06:54
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Originally we have
(1) L/S = 5/6
where L = Qty of Literature Books and S = Qty of Science books
And then we have
(2) (L+50)/(5*S/4) = 4/3
Note that S + S/4 = 4S/4 + S/4 = 5S/4
(2)=> 3*(L+50) = 4*5*S/4 ==> 3L + 150 = 5S
(1)=> 6L = 5S
(1) in (2) => 3L + 150 = 6L => 3L = 150 => L = 50
L in (1) => 6*50 = 5S => 6*10 = S = 60
Total ORIGINAL Qty of Books = 50 + 60 = 110 = ANSWER B.
(1) L/S = 5/6
where L = Qty of Literature Books and S = Qty of Science books
And then we have
(2) (L+50)/(5*S/4) = 4/3
Note that S + S/4 = 4S/4 + S/4 = 5S/4
(2)=> 3*(L+50) = 4*5*S/4 ==> 3L + 150 = 5S
(1)=> 6L = 5S
(1) in (2) => 3L + 150 = 6L => 3L = 150 => L = 50
L in (1) => 6*50 = 5S => 6*10 = S = 60
Total ORIGINAL Qty of Books = 50 + 60 = 110 = ANSWER B.
21 Apr 2023, 10:13
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A school library consists of literature books and science books in the ratio of 5:6. If 50 more literature books are added to the library and the number of science books is increased by 1/4th of the existing science books, the ratio of the literature books and science books increases to 4:3. If the library consists of only literature and the science books, what is the initial number of books in the library?
let literature books be L
and science books be S
then L:S is 5:6 or L = 5S/6 = 0.83S
After the addition of books, we have
(L+50)/1.25S is 4/3
=> L + 50 = 1.25S*4/3 = 1.67S
=> 0.83S + 50 = 1.67S
or S = 50/0.84 = 59.52 = 60 (approx)
L = 0.83*60 = 50 (approx)
so total number of books in the school library = 110
Answer B
let literature books be L
and science books be S
then L:S is 5:6 or L = 5S/6 = 0.83S
After the addition of books, we have
(L+50)/1.25S is 4/3
=> L + 50 = 1.25S*4/3 = 1.67S
=> 0.83S + 50 = 1.67S
or S = 50/0.84 = 59.52 = 60 (approx)
L = 0.83*60 = 50 (approx)
so total number of books in the school library = 110
Answer B
