A, B, C and D start a business with investments in a ratio 2:3:5:7. Rest of the problem in the question details?

Question

A, B, C and D start a business with investments in a ratio 2:3:5:7. After 4 months A invest the same amount as before, B and C withdrew half their investment and D withrew 4/9th of it's investment. What is the ratio of their profits at the end of the year?

Answer 1

Old Ratio

2:3:5:7

Because:

2+3+5+7=17

Old Profit Sharing Ratio

A = 2/17

B = 3/17

C = 5/17

D = 7/17

New Ratio Calculations

A = 2/17 * 1 = 2/17

B =  3/17 * (1 – 1/2) = 3/17 * 1/2 = 3/34

C = 5/17 * (1- 1/2) = 5/17 * 1/2  = 5/34

D = 7/17 * (1 – 4/9) = 7/17 * 5/9 = 35/153

 

Calculate Equivalent Ratios

A = 2/17 * 18/18 = 36/306

B =  3/34 * 9/9 = 27/306

C = 5/34 * 9/9 = 45/306

D = 35/153 * 2/2 = 70/306

New Profit-Sharing Ratio

Starting at the 5^th Month

A = 36/306

B =  27/306

C = 45/306

D = 70/306

36:27:45:70

Finding Profit Sharing At The End of the Year

Add

Old Ratio for  4 out of 12 months = 4/12 = 1/3

New Ratio for 8 out of 12  months = 8/12 = 2/3

Calculations

A =(2/17  * 1/3) + (2/17 * 2/3) = 2/51 + 4/51 = 6/51 = 2/17

B = (3/17 * 1/3) + (3/34 * 2/3) = 3/51 + 6/102 = 6/102 +6/102 = 12/102 = 4/34

C = (5/17 * 1/3) + (5/34 * 2/3) = 5/51 + 10/102 = 10/102 + 10/102 = 20/102 = 10/51

D = (7/17 * 1/3) + (35/153 * 2/3) = 7/51 + 70/459 = 63/459 + 70/459 = 133/459 = 133/459

Calculate Equivalent Ratios

A = 2/17 * 54/54 = 108/918

B =  4/34 * 27/27 = 108/918

C = 10/51 * 18/18 = 180/918

D = 133/459 * 2/2 = 266/918

108:108:180:266

Answer:

The ratio of their profits at the end of the year is

54:54:90:133

Answer 2

a:b:c:d = 2:3:5:7 initially

then after 4 months, b and c withdrew half their investment and D withdrew 4/9

what is the new ratio?

2:3/2: 5/2: 7-4/9(7)

2:1.5: 2.5: 7(5/9)

multiply by 18

36:27:45:70