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    ​The ratio of the number of students in the morning shift and the afternoon shift of a school was 13 : 9. After 'n' students moved from the morning sh
    Question

    The ratio of the number of students in the morning shift and the afternoon shift of a school was 13 : 9. After 'n' students moved from the morning shift to the afternoon shift, the said ratio became 19 : 14. Now 153 new students sought admission in the school, and these students joined the morning and the afternoon shifts in the ratio 6 : 11 respectively. If the ratio of the number of students in the morning shift and the afternoon shift of the school after the new admissions became 24 : 19, find the value of 'n'.

    A.

    36

    B.

    30

    C.

    24

    D.

    27

    Correct option is D

    Given:

    Initial ratio of students:

    Morning shift (M) : Afternoon shift (A) = 13 : 9

    After moving 'n' students from M to A, the new ratio becomes 19 : 14

    153 new students join in the ratio 6 : 11 (Morning : Afternoon).

    Final ratio after new admissions: 24 : 19

    Solution:

    Let initial students be M = 13x , A = 9x

    After transfer:

    13xn9x+n=1914\frac{13x - n}{9x + n} = \frac{19}{14}​​

    182x - 14n = 171x + 19n

    11x=33n x=3n11x = 33n \implies x = 3n​​

    New admissions:

    Morning: 54 , Afternoon: 99

    Final ratio:

    13(3n)n+549(3n)+n+99=2419\frac{13(3n) - n + 54}{9(3n) + n + 99} = \frac{24}{19}​​

    38n+5428n+99=2419\frac{38n + 54}{28n + 99} = \frac{24}{19}​​

    19(38n+54)=24(28n+99)19(38n + 54) = 24(28n + 99)​​

    50n=1350 n=2750n = 1350 \implies n = 27

    Thus the correct option is (d) 27.

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