Investment Ratio = Profit Sharing Ratio.
Ratio of Investments Hari : Giri = Rs.45000 : 54000 => 5 : 6.
Giri share = $\displaystyle 13200 \times \frac{6}{11}$ = Rs.7200
Hari share = $\displaystyle 13200 \times \frac{5}{11}$ = Rs.6000
As profit is 12.5% of the investment
Total investment = $\displaystyle \frac{20400}{12.5} \times 100$ = 163200.
Investment of Kumar = 163200 $\displaystyle \times \frac{8}{17}$ = Rs.76800.
Investment of Amar = 163200 $\displaystyle \times \frac{9}{17}$ = Rs.86400.
Ratio of investment, as investments is for different time.
Investment x Number of units of time.
Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.
X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.
Ratio of investments => X : Y : Z = 18 : 21 : 16.
Investment Ratio = Profit sharing Ratio.
Z = $\displaystyle 13750 \times \frac{16}{55}$ = Rs.4000.
Share of Z in the profit is Rs.4000.
Ratio of investments Kala : Sudha : Githa => 18000 : 24000 : 20000 => 9 : 12 : 10.
Investment x time.
Kala = 9 x 12 = 108.
Sudha = 12 x 12 = 144.
Githa = 10 x 9 = 180.
Or Kala : Sudha : Githa => 6 : 8 : 5.
Let shares of Kala, Sudha and Githa be = 6a : 8a : 5a.
Difference between the profits received by Kala and Sudha
6a – 8a = 2a = 840 or a = 420.
Githa = 5a = 5 x 420 = Rs.2100.
Let share of C be Rs.100, then B = C + 20% = 100 + 100 $\displaystyle \times \frac{20}{100}$ = Rs.120.
A = B + 10% => 120 + 120 $\displaystyle \times \frac{10}{100}$ = Rs.132.
Ratio of investments = A : B : C = 132 : 120 : 100 => 33 : 30 : 25.
B share in the profit = 36960 $\displaystyle \times \frac{30}{88}$ = Rs.12600.
Let Z investment be 100, then X = 130.
Let Y investment be 100, then X = 120.
Z : X_{1} : : X_{2} : Y = 100 : 130 : : 120 : 100 => 10 : 13 : : 12 : 10.
Z = Z x X_{2} = 10 x 12 = 120.
X = X_{1} x X_{2} = 13 x 12 = 156.
Y = X_{1} x Y = 13 x 10 = 130.
Therefore X : Y : Z = 156 : 130 : 120 or 78 : 65 : 60 = sum of units = 203.
Difference between X and Z = 78 – 60 => 18 units.
Total profit = $\displaystyle \frac{4140}{18} \times 203$ = Rs.46690.
Total profit = Rs.3800.
Jaya share = Rs.1400.
Kant share = Rs.3800 - Rs.1400 = Rs.2400.
Kant : Jaya = 2400 : 1400 => 12 : 7
Total profit = Rs.1800.
Suri share in the profit = Rs.720.
Giri share in the profit = Rs.1800 – Rs.720 = Rs.1080.
Ratio of shares = Giri : Suri = 1080 : 720 = 3 : 2.
Ratio of investments as investments is for different time
Investment x Time
Giri = Rs.30000 x 12 = Rs.360000.
Let Suri in the business for ‘a’ months.
Suri = Rs.32000 x a = Rs.32000a.
Rs.32000a = $\displaystyle \frac{360000}{3} \times 2$ = Rs.240000.
Suri = investment x Time = Rs.240000.
Time ‘a’ = $\displaystyle \frac{240000}{32000}$ = = 7.5 or 7 $\displaystyle \frac{1}{2}$ months.
Therefore Suri joined after 12 – 7 $\displaystyle \frac{1}{2} = 4 \frac{1}{2}$ months.
Ratio of shares Manu : Sunanda = 150000 : 175000 => 30 : 35 => 6 : 7.
Manu and Sunanda received equal profit then profit of each partner is $\displaystyle \frac{16800}{2}$ = Rs.8400.
Sunanda = Rs.8400, Manu = Profit + salary = Rs.8400.
Share of Manu excluding salary = $\displaystyle \frac{8400}{7} \times 6$ = Rs.7200.
Salary of Manu = Rs.8400 – Rs.7200 = Rs.1200.
Mukesh = 40000 x 12 = 480000.
Suresh = 50000 x 4 = 200000.
45000 x 8 = 360000 = 560000.
Ratio Mukesh : Suresh = 480000 : 560000 = 6 : 7.
Suresh = $\displaystyle 8450 \times \frac{7}{13}$ = Rs.4550.
Mukesh = $\displaystyle 8450 \times \frac{6}{13}$ = Rs.3900.
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