ExamVeda
Login
Home
41
Two friends invested Rs.1500 and Rs. 2500 in a business. They earned a profit of Rs. 800. One-half of the profit was divided equally between them and the other half was divided in proportion to their capitals. How much did each of them receive ?
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & {\text{Ratio of shares}} \cr & = 1500:2500 \cr & = 3:5 \cr & {\text{Share of first friend}} \cr & = {\text{Rs}}{\text{.}}\left[ {\frac{{400}}{2} + \left( {400 \times \frac{3}{8}} \right)} \right] \cr & = {\text{Rs}}.\left( {200 + 150} \right) \cr & = {\text{Rs}}{\text{. 350}} \cr & {\text{Share of second friend}} \cr & = {\text{Rs}}{\text{.}}\left[ {\frac{{400}}{2} + \left( {400 \times \frac{5}{8}} \right)} \right] \cr & = {\text{Rs}}.\left( {200 + 250} \right) \cr & = {\text{Rs}}{\text{. 450}} \cr} $$
42
Three persons stared a placement business with a capital of Rs. 3000. B invests Rs. 600 less than A and C invests Rs. 300 less than B. What is B's share in a profit of Rs. 886 ?
Discuss
Answer & Solution
Answer: Option C
Solution:
Let A's capital = Rs. x
Then, B's capital = Rs. (x - 600)
C's capital = Rs. (x - 600) - 300 = Rs. (x - 900)
∴ x + (x - 600) + (x - 900) = 3000
⇒ 3x = 4500
⇒ x = 1500
$$\eqalign{ & {\text{So, A}}:{\text{B}}:{\text{C}} \cr & = 1500:900:600 \cr & = 5:3:2 \cr & {\text{Hence, B's share}} \cr & = {\text{Rs}}{\text{.}}\left( {886 \times \frac{3}{{10}}} \right) \cr & = {\text{Rs}}{\text{. 265}}{\text{.80}} \cr} $$
43
X and Y are partners in a business. They invest in the ratio 5 : 6, at the end of 8 months X withdraws his capital. If they receive profits in the ratio of 5 : 9. Find how long Y's investment was used ?
Discuss
Answer & Solution
Answer: Option A
Solution:
Let Y's investment is used for T months → Now by using formula
$$\eqalign{ & \frac{{5 \times 8}}{{6 \times {{\text{T}}_2}}} = \frac{5}{9} \cr & {\text{T}} = 12{\text{ months}} \cr} $$
44
Four milkmen rented a pasture. M put to graze 16 cows for 3 months and N 20 cows for 4 months, O 18 cows for 6 months and P 42 cows for 2 months. If M's share of rent be Rs. 2400, the rent paid by O is ?
Discuss
Answer & Solution
Answer: Option D
Solution:
M graze 16 cows for 3 months.
N graze 20 cows for 4 months.
O graze 18 cows for 6 months.
P graze 42 cows for 2 months.
So, Ration of Rent
= M : N : O : P
= (16 × 3) : (20 × 4) : (18 × 6) : (42 × 2)
= 48 : 80 : 108 : 84
= 12 : 20 : 27 : 21
According to the question,
$$\eqalign{ & {\text{12 units}} = {\text{Rs}}{\text{. 2400}} \cr & {\text{1 unit}} = \frac{{2400}}{{12}} \cr & 27{\text{ units}} = \frac{{2400 \times 27}}{{12}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}5400 \cr} $$
45
Shankar starts a business with an investment of Rs. 120000. After three months, Aniket joined him with an invesment of Rs. 190000. They earned a profit of Rs. 1750000 after one year. What is Aniket's share in the profit ?
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & {\text{Shankar}}:{\text{Aniket}} \cr & = \left( {120000 \times 12} \right):\left( {190000 \times 9} \right) \cr & = 1440000:1710000 \cr & = 16:19 \cr & \therefore {\text{Aniket's share}} \cr & = {\text{Rs}}{\text{.}}\left( {1750000 \times \frac{{19}}{{35}}} \right) \cr & = {\text{Rs. }}{\text{950000 }} \cr} $$
46
Arun started a business investing Rs. 38000. After 5 months Bakul joined him with a capital of Rs. 55000. At the end of the year the total profit was Rs. 22000. What is the approximate difference between the share of profits Arun and Bakul ?
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & {\text{Arun}}:{\text{Bakul}} \cr & = \left( {38000 \times 12} \right):\left( {55000 \times 7} \right) \cr & = 456000:385000 \cr & = 456:385 \cr & \therefore {\text{Required difference}} \cr & = {\text{Rs}}{\text{.}}\,\left[ {22000 \times \left( {\frac{{456}}{{841}} - \frac{{385}}{{841}}} \right)} \right] \cr & = {\text{Rs}}{\text{.}}\left( {22000 \times \frac{{71}}{{841}}} \right) \cr & = {\text{Rs. }}{\text{1857}}{\text{.31}} \cr & = {\text{Rs. }}{\text{1857 }} \cr} $$
47
Goutam started a business with a sum of Rs. 60000. Jatin joined him 8 months later with a sum of Rs. 35000. At what respective ratio will the two share of profit after two years ?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{Gautam}}:{\text{Jatin}} \cr & = \left( {6000 \times 12} \right):\left( {35000 \times 8} \right) \cr & = 720000:280000 \cr & = 18:7 \cr} $$
48
Simran started a software business by investing Rs. 50000. After six months, Nanda joined her with a capital of Rs. 80000. After 3 years, they earned a profit of Rs. 24500. What was Simran's share in the profit ?
Discuss
Answer & Solution
Answer: Option E
Solution:
$$\eqalign{ & {\text{Simran}}:{\text{Nanda}} \cr & = \left( {50000 \times 36} \right):\left( {80000 \times 30} \right) \cr & = 1800000:2400000 \cr & = 3:4 \cr & \therefore \,{\text{Simran's share}} \cr & = {\text{Rs}}{\text{.}}\left( {24500 \times \frac{3}{7}} \right) \cr & = {\text{Rs. }}{\text{10500 }} \cr} $$
49
Dilip, Ram and Avtar started a shop by investing Rs. 2700, Rs. 8100 and Rs. 7200 respectively. At the end of one year, the profit earned was distributed. If Ram's share was Rs. 3600, what was their total profit ?
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & {\text{Dilip}}:{\text{Ram}}:{\text{Avtar}} \cr & = 2700:8100:7200 \cr & = 3:9:8 \cr & {\text{Let the total profit be Rs}}.\,x \cr & {\text{Then, Ram's share}} \cr & = {\text{Rs}}{\text{.}}\,\left( {\frac{9}{{20}}x} \right) \cr & \therefore \frac{9}{{20}}x = 3600 \cr & \Rightarrow x = \left( {\frac{{3600 \times 20}}{9}} \right) \cr & \Rightarrow x = 8000 \cr & {\text{Hence,}} \cr & {\text{Total profit}} = {\text{Rs}}{\text{. 8000}} \cr} $$
50
Aman started a business investing Rs. 70000. Rakhi joined him after six months with an amount of Rs. 105000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?
Discuss
Answer & Solution
Answer: Option B
Solution:
Aman : Rakhi : Sagar
= (70000 × 36) : (105000 × 30) : (140000 × 24)
= 12 : 15 : 16