15,000 is divided between Meera and Sheena in such a way that Sheena gets one-third of what Meera gets. Find: (i) The ratio between the shares of Meera and Sheena. (ii) The shares of Meera and Sheena.
The correct answer and explanation is:
Let the share of Meera be xx. According to the problem, Sheena gets one-third of what Meera gets, so Sheena’s share will be x3\frac{x}{3}.
The total amount to be divided is 15,000. Therefore, the equation becomes: x+x3=15000x + \frac{x}{3} = 15000
To solve for xx, first, multiply both sides of the equation by 3 to eliminate the fraction: 3x+x=450003x + x = 45000
Now, combine the terms on the left: 4x=450004x = 45000
Next, divide both sides by 4: x=450004=11250x = \frac{45000}{4} = 11250
So, Meera’s share is 11,250. Now, to find Sheena’s share, use the relationship x3\frac{x}{3}: Sheena’s share=112503=3750\text{Sheena’s share} = \frac{11250}{3} = 3750
(i) The ratio between the shares of Meera and Sheena:
The ratio of Meera’s share to Sheena’s share is: 112503750=3:1\frac{11250}{3750} = 3:1
(ii) The shares of Meera and Sheena:
- Meera’s share = 11,250
- Sheena’s share = 3,750
Explanation:
The problem can be solved using algebra by setting up an equation based on the total amount of 15,000. By defining Meera’s share as xx, it is possible to express Sheena’s share in terms of xx. This allows us to solve for xx, and then calculate both Meera’s and Sheena’s shares. Finally, the ratio is derived by dividing the two shares.