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
- ₹28,000 were divided among A, B and C, such that 2 times the share of A = 9 times the share of B = 6 times the share of C. Find the share of A.
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- What is the simplest form of the ratio of $6\text{ h} : 3\text{ days}$?
- Two natural numbers are in the ratio of $6 : 8$ and their product is $768$. The smaller of the numbers is:
- Two numbers are in the ratio 2 : 3; if 20 is added to 20% of the smaller number, it will be equal to 10% of the larger number plus 25. Then, the smaller number is: _______.
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Important Questions from Ratio and Proportion
The cost of a diamond is directly proportional to the square of its weight. The cost of a 14 gm diamond is Rs. 2560. This diamond got broken down into two pieces in the ratio of 5 ∶ 9. How much loss percent is incurred due to this breakage ? (Correct to two decimal places)
Atul purchased Bread costing Rs.20 and gave a 100 rupee note to the shopkeeper. The shopkeeper gave the balance money in coins of denomination Rs.2, Rs.5 and Rs.10. If these coins are in the ratio 5 ∶ 4 ∶ 1, then how many Rs.5 coins did the shopkeeper give?
A person divides a certain amount among his three sons in the ratio of 3 ∶ 4 ∶ 5. If he had divided this amount in the ratio of 1/3,1/4,1/5, his son, who had got the lowest share earlier, would get Rs.1,188 more. Find the amount (in Rs).
In a school 3/8 of the number of students are girls and the rest are boys. One-third of the number of boys are below 10 years and 2/3 the number if girls are also below 10 years. If the number of students of age 10 or more years is 260. then the number of boys in the school is:
If a : b : c = \(\frac{1}{4} : \frac{1}{3} : \frac{1}{2}, \) then \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
