After 10 years, Ajay will be two times as old as Bhushan is today. Five years ago, Chandru was younger than Bhushan by 10 years. After 5 years, Ajay will be seven times as old as Chandru was five years ago. What is the sum of the current ages of Ajay, Bhushan and Chandru? (All ages are in years)Enter your response (as an integer) using the virtual keyboard in the box provided below.
Question
After 10 years, Ajay will be two times as old as Bhushan is today. Five years ago, Chandru was younger than Bhushan by 10 years. After 5 years, Ajay will be seven times as old as Chandru was five years ago. What is the sum of the current ages of Ajay, Bhushan and Chandru? (All ages are in years)Enter your response (as an integer) using the virtual keyboard in the box provided below.
Solution
Let's denote the current ages of Ajay, Bhushan, and Chandru as A, B, and C respectively.
From the problem, we have the following equations:
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A + 10 = 2B (After 10 years, Ajay will be two times as old as Bhushan is today)
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C - 5 = B - 10 (Five years ago, Chandru was younger than Bhushan by 10 years)
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A + 5 = 7(C - 5) (After 5 years, Ajay will be seven times as old as Chandru was five years ago)
Now, we can solve these equations step by step:
From equation 2, we get B = C + 5.
Substitute B in equation 1, we get A + 10 = 2(C + 5), which simplifies to A = 2C + 10.
Substitute A and B in equation 3, we get 2C + 10 + 5 = 7(C - 5), which simplifies to C = 20.
Substitute C = 20 in equation 1 and 2, we get A = 50 and B = 25.
So, the sum of the current ages of Ajay, Bhushan and Chandru is A + B + C = 50 + 25 + 20 = 95.
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