Arjit's age is 3 years more than 1.5 times the age of Heera, whose age is 10 years more than (\frac{2}{3}) the age of Deepika. If 5 times the age of Deepika is equal to 3 times the age of Arjit, what is the sum of the present ages of all three?
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99 years
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95 years
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100 years
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97 years
C
Correct answer
Explanation
Let D = Deepika's age. Heera = (2/3)D + 10. Arjit = 1.5 × Heera + 3 = 1.5((2/3)D + 10) + 3 = D + 15 + 3 = D + 18. Given: 5D = 3 × Arjit = 3(D + 18) = 3D + 54. So 5D = 3D + 54, meaning 2D = 54, thus D = 27. Heera = (2/3)(27) + 10 = 18 + 10 = 28. Arjit = 27 + 18 = 45. Sum = 27 + 28 + 45 = 100 years.