# Rohit says to Ajay, “Give me a hundred, I shall then become twice as rich as you”. Ajay replies, “if you give ten, I shall be six times as rich as you.” How much does each have originally?

Last updated date: 18th Mar 2023

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Answer

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Hint – In this problem two statements were given to us as the saying of Rohit and Ajay to each other. So let the total amount with Rohit and with Ajay be some variable and use the information provided in the question to find out these variables.

“Complete step-by-step answer:”

Let the amount Rohit have x Rs.

And the amount Ajay has y Rs.

Case 1 – Rohit says to Ajay, ‘Give me a hundred, I shall then become twice as rich as you.’

So, construct this information into linear equation we have,

$ \Rightarrow x + 100 = 2\left( {y - 100} \right)$……………………….. (1)

Case 2 – Ajay replies, ‘If you give me ten, I shall be six times as rich as you.’

So, construct this information into linear equation we have,

$ \Rightarrow y + 10 = 6\left( {x - 10} \right)$……………………. (2)

Now solve, these two equations using substitution method we have,

From equation (2) $y = 6x - 70$ so, substitute this value in equation (1) we have,

$ \Rightarrow x + 100 = 2\left( {6x - 70 - 100} \right)$

Now simplify the above equation we have,

$ \Rightarrow x + 100 = 12x - 340$

$ \Rightarrow 11x = 440$

Now divide by 11 we have,

$ \Rightarrow x = \frac{{440}}{{11}} = 40$ Rs.

Now from equation (2) we have

$y = 6x - 70 = 6 \times 40 - 70 = 240 - 70 = 170$ Rs.

So, Rohit has 40 Rs. And Ajay has 170 Rs.

Hence, option (c) is correct.

Note – Whenever we face such types of problems the key concept is to formulate the mathematical equation using the information provided in the question. Then use these equations to find out the value of these variables. This concept will help you get on the right track to reach the solution.

“Complete step-by-step answer:”

Let the amount Rohit have x Rs.

And the amount Ajay has y Rs.

Case 1 – Rohit says to Ajay, ‘Give me a hundred, I shall then become twice as rich as you.’

So, construct this information into linear equation we have,

$ \Rightarrow x + 100 = 2\left( {y - 100} \right)$……………………….. (1)

Case 2 – Ajay replies, ‘If you give me ten, I shall be six times as rich as you.’

So, construct this information into linear equation we have,

$ \Rightarrow y + 10 = 6\left( {x - 10} \right)$……………………. (2)

Now solve, these two equations using substitution method we have,

From equation (2) $y = 6x - 70$ so, substitute this value in equation (1) we have,

$ \Rightarrow x + 100 = 2\left( {6x - 70 - 100} \right)$

Now simplify the above equation we have,

$ \Rightarrow x + 100 = 12x - 340$

$ \Rightarrow 11x = 440$

Now divide by 11 we have,

$ \Rightarrow x = \frac{{440}}{{11}} = 40$ Rs.

Now from equation (2) we have

$y = 6x - 70 = 6 \times 40 - 70 = 240 - 70 = 170$ Rs.

So, Rohit has 40 Rs. And Ajay has 170 Rs.

Hence, option (c) is correct.

Note – Whenever we face such types of problems the key concept is to formulate the mathematical equation using the information provided in the question. Then use these equations to find out the value of these variables. This concept will help you get on the right track to reach the solution.

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