​If A exceeds B by 40% and B is less than C by 20%, then find A:C​

Correct option is D

Given:

1. A exceeds B by 40%.

2. B is less than C by 20%.

We need to find the ratio A : C .

Formula Used:

1. If A exceeds B by x% :

A = $$B \times \left(1 + \frac{x}{100}\right)$$​​

2. If B is less than C by y% :

B = $$C \times \left(1 - \frac{y}{100}\right)$$​​

Solution:

1. **Express A in terms of B :**

A = $$B \times \left(1 + \frac{40}{100}\right)$$​​

Simplify:

A = B $$\times$$​ 1.4

2. **Express B in terms of C :**

B = $$C \times \left(1 - \frac{20}{100}\right)$$​​

Simplify:

B = C $$\times$$​ 0.8

3. $$Substitute B = C \times 0.8 into A = B \times 1.4$$​:

A = $$(C \times 0.8) \times 1.4$$​​

Simplify:

A = $$C \times (0.8 \times 1.4)$$​​

A = $$C \times 1.12$$​​

4. **Find the ratio A : C :**

A : C = 1.12 : 1

To express as a whole number ratio, multiply both sides by 100:

A : C = 112 : 100

Simplify:

A : C = 28 : 25

Final Answer:

The ratio A : C is **28 : 25**.