In the following table of inverse variations, what are the values of A, B and C respectively? M 15 -6 2 C N -4 A B 60
10, -30, -1
Understanding Inverse Variation in the Given Table
This question requires us to determine the missing values (A, B, and C) in a table that demonstrates an inverse variation. An inverse variation occurs when the product of two quantities remains constant. If we denote the two quantities as M and N, their relationship can be written as:
\( M \times N = k \)
Here, k represents the constant of variation.
Analyzing the Data Table for Inverse Variation
The problem presents the following data, which we can format to better understand the relationships:
| M | 15 | -6 | 2 | C |
| N | -4 | A | B | 60 |
We need to find the values of A, B, and C using the principle of inverse variation.
Step 1: Calculate the Constant of Variation (k)
To find the constant of variation, k, we use a pair of values where both M and N are provided. From the first column of the table, we have M = 15 and N = -4.
Using the formula for inverse variation:
\( k = M \times N \)
Substitute the known values:
\( k = 15 \times (-4) \)
\( k = -60 \)
Thus, the constant of variation for this table is -60.
Step 2: Determine the Value of A
We use the constant k = -60 to find A. According to the table, when M = -6, N = A.
Applying the inverse variation formula:
\( M \times N = k \)
\( (-6) \times A = -60 \)
To solve for A, we divide both sides by -6:
\( A = \frac{-60}{-6} \)
\( A = 10 \)
Step 3: Determine the Value of B
Similarly, we use k = -60 to find B. The table shows that when M = 2, N = B.
Using the formula:
\( M \times N = k \)
\( 2 \times B = -60 \)
To solve for B, we divide both sides by 2:
\( B = \frac{-60}{2} \)
\( B = -30 \)
Step 4: Determine the Value of C
Finally, we use k = -60 to find C. The table indicates that when M = C, N = 60.
Using the formula:
\( M \times N = k \)
\( C \times 60 = -60 \)
To solve for C, we divide both sides by 60:
\( C = \frac{-60}{60} \)
\( C = -1 \)
Summary of Calculated Values
We have found the following values for A, B, and C:
- A = 10
- B = -30
- C = -1
Therefore, the values of A, B, and C respectively are 10, -30, and -1.
Matching with Provided Options
Let's compare our results with the given options:
- Option 1: 10, -30, -1
- Option 2: 10, -1, 30
- Option 3: -30, 10, -1
- Option 4: -1, -30, 10
Our calculated values (A=10, B=-30, C=-1) match Option 1.
Similar Questions
What number must be subtracted from both the numerator and denominator of the fraction 27/35 so that it becomes 2/3?
If a, b, c, d, e and f satisfy
2a = 3b = 6c = 9d = 12e = 18f, then what is the value of (a + b)/(c + d + e + f)?
To maintain 8 cows for 60 days, a milkman spends Rs. 6400. To maintain 5 cows for n days, he spends Rs. 4800. What is the value of n?
4 goats or 6 sheep can graze a field in 50 days. 2 goats and 3 sheep will graze it in
There are 350 boys in the first three standard. The ratio of the number of boys in first and second standards is 2 : 3, while the ratio of boys in second and third standard is 4 : 5. What is the total number of boys in first and third standards?
The annual incomes of two persons are in the ratio 9 ∶ 7 and their expenses are in the ratio 4 ∶ 3. If each of them saves Rs. 2000 per year, what is the difference in their annual incomes?
In a class of 49 students, the ratio of girls to boys is 4 ∶ 3. If 4 girls leave the class, the ratio of girls to boys would be
When a ball is allowed to fall, the time it takes to fall any distance varies as the square root of the distance and it takes 4 seconds to fall 78.40 m. How long would it take to fall 122.50 m?
Incomes of Mahesh and Kamal are in the ratio 1 : 2 and their expenses are in the ratio 1 : 3. Which one of the following is correct?
In an office, one-third of the workers are women, half of the women are married, and one-third of the married women have children. If three-fourth of the men are married and one-third of the married men have children, then what is the ratio of married women to married men?
Important Questions from Simple Ratios
If the value of \(\frac{{p - q}}{q} = \frac{4}{3}\) .find p : q
Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct ?
The two numbers are in the ratio of 9 ∶ 7 and the difference between of these two number is 6000. What is the sum of the two numbers?
A certain number is added to each of a pair of numbers which are in the ratio 4 ∶ 5. The sum of the resulting numbers is 39 and their ratio (taken in the same order as mentioned above) is 6 ∶ 7. What is the number added?
If (p + q) ∶ (q + r) ∶ (r + p) = 5 ∶ 6 ∶ 7 and p + q + r = 18, find the value of p ∶ q ∶ r
