Ratio Problem: Calculate Arun's Initial Money
This problem requires finding an initial sum of money based on initial and final ratios after a transfer.
Initial Ratio Representation
Let the initial amounts Arun and Ahaan had be $9x$ and $5x$, representing the $9:5$ ratio.
Amounts After Transfer
When Arun gives ₹12 to Ahaan:
- Arun's money becomes: $9x - 12$
- Ahaan's money becomes: $5x + 12$
Forming the Ratio Equation
The new ratio is $4:3$. This gives the equation:
$ \frac{9x - 12}{5x + 12} = \frac{4}{3} $
Solving for the Variable x
Cross-multiply to solve the equation:
$ 3(9x - 12) = 4(5x + 12) $
$ 27x - 36 = 20x + 48 $
Group terms with $x$ and constants:
$ 27x - 20x = 48 + 36 $
$ 7x = 84 $
Calculate $x$:
$ x = \frac{84}{7} = 12 $
Calculating Arun's Initial Money
Arun's initial amount was $9x$. Substitute the value of $x$:
Initial Amount = $9 \times 12$
$ 9 \times 12 = 108 $
Arun initially had ₹108.
Similar Questions
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Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
