Finding the Smaller Natural Number
We are given two natural numbers in the ratio $6:8$. Let these numbers be represented as $6x$ and $8x$, where $x$ is a common positive multiplier.
The product of these two numbers is stated to be $768$. We can set up the equation based on this information:
$ (6x) \times (8x) = 768 $
Simplify the multiplication on the left side:
$ 48x^2 = 768 $
To find the value of $x$, first isolate $x^2$ by dividing both sides by $48$:
$ x^2 = \frac{768}{48} $
$ x^2 = 16 $
Now, solve for $x$ by taking the square root of both sides:
$ x = \sqrt{16} $
$ x = 4 $
Since we are dealing with natural numbers, we consider the positive value of $x$. The two numbers are:
- First number: $6x = 6 \times 4 = 24$
- Second number: $8x = 8 \times 4 = 32$
The question asks for the smaller of these two numbers. Comparing $24$ and $32$, the smaller number is $24$.
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 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 \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
