A reward of Rs. 1800 is shared by Riya and Kabir in the ratio 4:5. Find the amount received by Riya and Kabir, respectively.

The correct answer is Rs. 800, Rs. 1000.

Step 1: Identify the given information.
Total reward amount = Rs. 1800
Ratio of sharing between Riya and Kabir = 4 : 5

Step 2: Find the total number of ratio parts.
To divide the total reward according to the ratio 4 : 5, add the parts of the ratio together:

$\text{Total parts}=4+5=9$

Step 3: Determine the value of one part.
Divide the total reward by the total number of parts:

$\text{Value of 1 part}=\frac{1800}{9}=\text{Rs. 200}$

Step 4: Calculate the individual share for each person.
Riya's share corresponds to 4 parts of the ratio:

$\text{Amount received by Riya}=4\times 200=\text{Rs. 800}$

Kabir's share corresponds to 5 parts of the ratio:

$\text{Amount received by Kabir}=5\times 200=\text{Rs. 1000}$

Thus, the amounts received by Riya and Kabir are Rs. 800 and Rs. 1000, respectively.