Solving for Ratio A:C
We are given two conditions relating quantities A, B, and C:
- A exceeds B by 25%: This can be written mathematically as $A = B + 0.25B$, which simplifies to $A = 1.25B$.
- B is less than C by 30%: This can be written as $B = C - 0.30C$, simplifying to $B = 0.70C$.
Calculating the Ratio A to C
Our goal is to find the ratio of A to C, which is $A : C$. We can achieve this by substituting the expression for B from the second condition into the first condition.
- Start with the equation for A: $A = 1.25B$.
- Substitute $B = 0.70C$ into the equation: $A = 1.25 \times (0.70C)$.
- Perform the multiplication: $1.25 \times 0.70 = \frac{125}{100} \times \frac{70}{100} = \frac{5}{4} \times \frac{7}{10} = \frac{35}{40}$.
- Simplify the fraction: $\frac{35}{40} = \frac{7}{8}$.
- So, we have $A = \frac{7}{8}C$.
This equation shows that A is $\frac{7}{8}$ of C. Therefore, the ratio of A to C ($A : C$) is $7 : 8$.
Similar Questions
- If A : B = 3 : 5 and B : C = 4 : 7, then the value of A : B : C is:
- If $a : b :: 3 : 4$ then the value of the expression $\frac{5a - 3b}{7a + 2b}$ is:
- If the third proportional of 8 and 20 be x, then what is the value of x?
- If $0.75 : x :: 25 : 8$, then what is the value of $x$?
- If $a : b = 7 : 9$ and $b : c = 1 : 12$, then $a : b : c$ is:
- If $\frac{A}{4} = \frac{B}{5} = \frac{C}{6}$, then $A : B : C$ is:
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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:
