Ratio Weights Calculation
Let the original weights of the three friends be $7x$, $8x$, and $9x$ kg, based on the initial ratio 7:8:9.
Weight Gain Analysis
Each friend gains 5 kg. Their new weights become:
- Friend 1: $7x + 5$ kg
- Friend 2: $8x + 5$ kg
- Friend 3: $9x + 5$ kg
New Ratio Equation
The new weights are in the ratio 12:13:14. We can set up an equation using any two parts of this ratio. Let's use the first two:
$ \frac{7x + 5}{12} = \frac{8x + 5}{13} $
Solving for Variable x
Cross-multiply to solve the equation:
$ 13(7x + 5) = 12(8x + 5) $
$ 91x + 65 = 96x + 60 $
Rearrange the terms to solve for $x$:
$ 65 - 60 = 96x - 91x $
$ 5 = 5x $
$ x = 1 $
Heaviest Friend's Original Weight
The original weights correspond to the ratio 7:8:9. The heaviest friend has the largest share, represented by $9x$. Substitute the value of $x$ found:
Original weight of the heaviest friend = $9x = 9(1) = 9$ kg.
Similar Questions
- A ribbon is cut into three pieces in the ratio 2:3:5. If the length of the longest piece is 20 cm, what is the total length of the ribbon?
- Three numbers are in the ratio 2:3:5. If their average is 100, what is the difference between the largest and the smallest number?
- Three numbers are such that the second is 150% of the first, and the third is 80% of the second. What is the ratio of the first to the third?
- Three friends share a winning prize in the ratio 2:3:4. If the total prize is Rs. 9000, how much more does the person with the highest share get than the lowest?
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Rs. 640 shared among 8 people. 2 back out. What's new share per person?
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 \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
