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Question Number 87553 by TawaTawa1 last updated on 05/Apr/20

Answered by ajfour last updated on 05/Apr/20

$$letno.ofboysinA=3k$$$$...........girls....A=2k$$$$letno.ofgirlsinB=x$$$$\mathrm{\&}no.ofboysinB=y$$$$no.ofgirlsinC=z$$$$no.ofboysinC=t$$$$\Rightarrow x+y=5k...\left(i\right)$$$$\frac{x}{4}+z=16+x...\left(ii\right)$$$$\frac{y}{t}=\frac{5}{8}....\left(iii\right)$$$$z+t=100....\left(iv\right)$$$$10k+100=220...\left(v\right)$$$$Q=\frac{3k+y+t}{2k+x+z}=?$$$$from\left(v\right):k=12$$$$\Rightarrow x+y=60\left[using\left(i\right)\right]$$$$z=100-t$$$$y=\frac{5t}{8}$$$$Nowfrom\left(ii\right)$$$$\frac{x}{4}+100-t=16+x$$$$\Rightarrow \frac{3x}{4}+t=84...\left(I\right)$$$$x+\frac{5t}{8}=60....\left(II\right)$$$$\Rightarrow 336-4t+\frac{15t}{8}=180$$$$\frac{17t}{8}=156$$$$buttshudhavbeenaninteger!$$$$Ishallcheckgainafterawhile..$$

Commented by TawaTawa1 last updated on 05/Apr/20

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}.$$$$\mathrm{From}\mathrm{your}\mathrm{solution}\mathrm{sir}.\mathrm{I}\mathrm{got}7:4$$

Commented by TawaTawa1 last updated on 05/Apr/20

$$\mathrm{I}\mathrm{said}\mathrm{let}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{students}\mathrm{be}=\mathrm{x}$$$$\mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{boys}\mathrm{be}=\mathrm{p}$$$$\mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{girls}=\mathrm{q}$$$$\mathrm{So}\mathrm{that},\mathrm{p}+\mathrm{q}=\mathrm{x}$$$$\mathrm{No}\mathrm{of}\mathrm{boys}\mathrm{and}\mathrm{girls}\mathrm{in}\mathrm{A}=\frac{3\mathrm{x}}{5}\mathrm{and}\frac{2\mathrm{x}}{5}$$$$\mathrm{Number}\mathrm{of}\mathrm{girls}\mathrm{in}\mathrm{B}=0.25\mathrm{q}$$$$\mathrm{Number}\mathrm{of}\mathrm{girls}\mathrm{in}\mathrm{C}=0.25\mathrm{q}+16$$$$\mathrm{Number}\mathrm{of}\mathrm{boys}\mathrm{in}\mathrm{B}\mathrm{and}\mathrm{C}=\frac{5\mathrm{x}}{13}\mathrm{and}\frac{8\mathrm{x}}{13}$$$$\mathrm{And}100\mathrm{students}\mathrm{in}\mathrm{C}(\mathrm{no}\mathrm{of}\mathrm{boys}+\mathrm{number}\mathrm{of}\mathrm{girls})$$$$\frac{8\mathrm{x}}{13}+0.25\mathrm{q}+16=100$$$$\frac{8\mathrm{x}}{13}+0.25\mathrm{q}=84.......\left(\mathrm{i}\right)$$$$\mathrm{Number}\mathrm{of}\mathrm{students}\mathrm{in}\mathrm{B}(\mathrm{Boys}+\mathrm{Girls})$$$$\frac{5\mathrm{x}}{13}+0.25\mathrm{q}=60......\left(\mathrm{ii}\right)$$$$\mathrm{Then}\mathrm{solving}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right)\mathrm{q}=80$$$$\mathrm{And}\mathrm{p}=220-80=140$$$$\mathrm{Hence},\mathrm{p}:\mathrm{q}=140:80\Rightarrow 7:4$$$$$$$$\mathrm{It}\mathrm{is}\mathrm{the}60\mathrm{you}\mathrm{got}\mathrm{that}\mathrm{made}\mathrm{me}\mathrm{to}\mathrm{solve}\mathrm{further}.$$$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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