Answer: Option 'E' is correct.
Step-by-step explanation:
Since we have given that
Let the total number of gongs be 'g'.
Number of ten inch gongs = 18
Let the number of 12 inch gongs be 'x'.
Let the number of 15 inch gongs be 'y'.
so, equation would be
![18+x+y=g](https://tex.z-dn.net/?f=18%2Bx%2By%3Dg)
Half of the gongs are tiger gongs is given by
![t=\dfrac{g}{2}\\\\g=2t](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7Bg%7D%7B2%7D%5C%5C%5C%5Cg%3D2t)
Half of the 12 inch gongs are not tiger gongs
so, number of tiger gongs which is of 12 inch = ![\dfrac{x}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B2%7D)
Among the tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch.
![\dfrac{x}{2}+\dfrac{x}{2}+\dfrac{x}{2}=t\\\\\dfrac{3x}{2}=t](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B2%7D%2B%5Cdfrac%7Bx%7D%7B2%7D%2B%5Cdfrac%7Bx%7D%7B2%7D%3Dt%5C%5C%5C%5C%5Cdfrac%7B3x%7D%7B2%7D%3Dt)
Half of the gongs are of 15 inch is given by
![y=\dfrac{g}{2}\\\\2y=g](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7Bg%7D%7B2%7D%5C%5C%5C%5C2y%3Dg)
Since we have
![g=2t\\\\g=2\times \dfrac{3x}{2}\\\\g=3x\\\\\dfrac{g}{3}=x](https://tex.z-dn.net/?f=g%3D2t%5C%5C%5C%5Cg%3D2%5Ctimes%20%5Cdfrac%7B3x%7D%7B2%7D%5C%5C%5C%5Cg%3D3x%5C%5C%5C%5C%5Cdfrac%7Bg%7D%7B3%7D%3Dx)
so, According to question, it becomes,
![18+\dfrac{g}{2}+\dfrac{g}{3}=g\\\\18+\dfrac{5g}{6}=g\\\\18=g-\dfrac{5g}{6}\\\\18=\dfrac{6g-5g}{6}=\dfrac{g}{6}\\\\18\times 6=g\\\\108=g](https://tex.z-dn.net/?f=18%2B%5Cdfrac%7Bg%7D%7B2%7D%2B%5Cdfrac%7Bg%7D%7B3%7D%3Dg%5C%5C%5C%5C18%2B%5Cdfrac%7B5g%7D%7B6%7D%3Dg%5C%5C%5C%5C18%3Dg-%5Cdfrac%7B5g%7D%7B6%7D%5C%5C%5C%5C18%3D%5Cdfrac%7B6g-5g%7D%7B6%7D%3D%5Cdfrac%7Bg%7D%7B6%7D%5C%5C%5C%5C18%5Ctimes%206%3Dg%5C%5C%5C%5C108%3Dg)
Hence, Option 'e' is correct.