# [Solved] Ivan and Tanya share £150 in a ratio of 4: 1. Work out how much more Ivan gets compared to Tanya

**Ivan and Tanya share £150 in a ratio of 4: 1. Work out how much more Ivan gets compared to Tanya.**

**Step 1: Understand the problem**

Ivan and Tanya share £150 in a ratio of 4:1. We need to find out how much more Ivan gets compared to Tanya.

**Step 2: Find the total number of parts in the ratio**

The ratio of Ivan’s share to Tanya’s share is 4:1. To find the total number of parts in the ratio, we add the values of the two parts:

4 + 1 = 5

This means that the £150 is divided into 5 parts.

**Step 3: Find the value of one part**

To find the value of one part, we divide the total amount (£150) by the total number of parts (5):

£150 ÷ 5 = £30

So, one part of the ratio is worth £30.

**Step 4: Find Ivan’s and Tanya’s shares**

We can find out how much Ivan and Tanya each get by multiplying their respective parts by the value of one part:

Ivan’s share = 4 parts × £30/part = £120 Tanya’s share = 1 part × £30/part = £30

Therefore, Ivan gets £120 – £30 = £90 more than Tanya.

**Step 5: Check the answer**

We can check the answer by verifying that the ratio of Ivan’s share to Tanya’s share is indeed 4:1:

Ivan’s share / Tanya’s share = £120 / £30 = 4

This confirms that Ivan gets four times the amount that Tanya gets, which is what we expect from a ratio of 4:1.

**Therefore, Ivan gets £90 more than Tanya.**

**Concept used**

The concept used in this problem is **proportion and ratio.** The total amount is divided into parts according to the given ratio, and then each part is multiplied by a common factor to find the actual amount for each part.

The difference between the parts is then calculated to find the difference in the amount received by each person.

**Step-by-Step Explanation**

**Step 1**

The ratio of Ivan and Tanya’s shares is 4:1, which means Ivan gets 4 parts and Tanya gets 1 part.

**Step 2**

To find out how much each part is worth, we divide the total amount (£150) by the sum of the ratio (4 + 1 = 5). This gives us £30 per ratio point.

**Step 3**

To determine how much Ivan gets, we multiply the £30 per ratio point by the number of ratio points in Ivan’s share (4). This gives us £120.

**Step 4**

To determine how much Tanya gets, we multiply the £30 per ratio point by the number of ratio points in Tanya’s share (1). This gives us £30.

**Step 5**

To find out how much more Ivan gets compared to Tanya, we subtract Tanya’s share (£30) from Ivan’s share (£120). This gives us £90.

So Ivan gets £90 more than Tanya.

**Therefore the answer is £90.**

## Method 2

**Solution: **Given that Ivan and Tanya share in a ratio of 4:1.

Let 4x be Ivan’s money and x be Tanya’s money.

According to the question.

4x + x = 50

5x = 150

x = 30

We know that Ivan gets 4x money.

Substituting the value of x, we get

4(30) = £120

⟹Ivan gets four parts, i.e. £120, and Tanya gets 1 part, i.e. £30

Now, the difference between the share of Ivan and Tanya

£120 – £30

£90

**Hence, Ivan gets £90 more than Tanya**.

## Conclusion

**Ivan and Tanya share £150 in a ratio of 4: 1. Ivan gets £90 more than Tanya.**