Shift and Ratio of Students

Question

The ratio of the number of students in the morning shift and afternoon shift of a school was $13 : 9$. After $21$ students moved from the morning shift to the afternoon shift, this ratio became $19 : 14$. Next, some new students joined the morning and afternoon shifts in the ratio $3 : 8$ and then the ratio of the number of students in the morning shift and the afternoon shift became $5 : 4$. The number of new students who joined is

Accepted Answer

D. Let initial morning and afternoon students be $13x$ and $9x$. After $21$ students moved: $$\frac{13x - 21}{9x + 21} = \frac{19}{14}$$ $$14(13x - 21) = 19(9x + 21)$$ $$182x - 294 = 171x + 399 \implies 11x = 693 \implies x = 63$$ So, after the move: Morning $= 13(63) - 21 = 819 - 21 = 798$ Afternoon $= 9(63) + 21 = 567 + 21 = 588$ Let new students joining be $3k$ and $8k$ (total $= 11k$): $$\frac{798 + 3k}{588 + 8k} = \frac{5}{4}$$ $$4(798 + 3k) = 5(588 + 8k)$$ $$3192 + 12k = 2940 + 40k \implies 28k = 252 \implies k = 9$$ Total new students $= 11k = 11 	imes 9 = 99$.

Answer

110

Answer

121

Answer

88

Answer

99

Shift and Ratio of Students

Explanation

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