To solve this problem, let's break down the given information and derive the answer step-by-step:
1. Let's denote the mass of the papaya by [tex]\( P \)[/tex] kg.
2. According to the problem, the durian is 4 times as heavy as the papaya. Therefore, the mass of the durian can be expressed as [tex]\( D = 4P \)[/tex] kg.
3. It's also given that the durian is heavier than the papaya by 1 kg 260 g. We need to convert 1 kg 260 g to kilograms:
[tex]\[
1 \text{ kg} + 260 \text{ g} = 1 \text{ kg} + 0.260 \text{ kg} = 1.260 \text{ kg}
\][/tex]
4. Now, let's set up an equation based on this information. The difference in their masses is given as 1.260 kg:
[tex]\[
D - P = 1.260 \text{ kg}
\][/tex]
5. We have already expressed [tex]\( D \)[/tex] as [tex]\( 4P \)[/tex]:
[tex]\[
4P - P = 1.260 \text{ kg}
\][/tex]
6. Simplify the equation:
[tex]\[
3P = 1.260 \text{ kg}
\][/tex]
7. Solving for [tex]\( P \)[/tex]:
[tex]\[
P = \frac{1.260 \text{ kg}}{3}
\][/tex]
[tex]\[
P = 0.420 \text{ kg}
\][/tex]
Hence, the mass of the papaya is 0.420 kg.
8. To find the mass of the durian, we use the relationship [tex]\( D = 4P \)[/tex]:
[tex]\[
D = 4 \times 0.420 \text{ kg}
\][/tex]
[tex]\[
D = 1.680 \text{ kg}
\][/tex]
So, the masses of the fruits are:
- Papaya: 0.420 kg
- Durian: 1.680 kg
In conclusion, the mass of the papaya is [tex]\( \boxed{0.42} \)[/tex] kg and the mass of the durian is 1.68 kg.
