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An amount is divided between two partners in the ratio 3:5. If the second partner receives 40 more than the first, what is the total amount divided?
160
200
240
320
160
Given: Ratio of shares between two partners is 3:5. The second partner receives 40 more than the first partner.
Ratio of shares between two partners is 3:5. The second partner receives 40 more than the first partner.
Total┬аAmount=(Part┬а1+Part┬а2)├ЧUnit┬аValue
Calculate the difference in ratio parts (5тИТ3=2 units). Since 2 units represent 40, 1 unit equals 20. The total is 3+5=8 units, so 8├Ч20=160.
Many students mistake the '40 more' as the total amount or calculate only one partner's share instead of the total sum.
Define ratio parts
Let the shares of the two partners be 3x and 5x respectively.
3x,5x
Set up the equation based on the difference
The second partner receives 40 more than the first, which gives the equation 5xтИТ3x=40.
2x=40
Solve for x
Divide the difference by the ratio gap to find the value of one part.
x=240тАЛ=20
Calculate total amount
The total amount is the sum of both parts, 3x+5x=8x. Substituting x=20, we get 8├Ч20=160.
8├Ч20=160
A is correct because the total sum of the ratio parts 8x equates to 160 when x=20.
This unit-based ratio approach is applicable across all Profit and Loss, Partnership, and Mixture/Alligation problems to avoid complex algebraic equations.