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31. Yogesh started a business investing Rs. 45000. After 3 months, Pranab joined him with a capital of Rs. 60000. After another 6 months, Atul joined them with a capital of Rs. 90000. At the end of the year, they made a profit of Rs. 20000. What would be Atuls share in it?

A. Rs. 7000

B. Rs. 6000

C. Rs. 5000

D. Rs. 4000

Discuss

Solution:

Just take care of the months of investment, rest all will be simple.
Yogesh : Pranab : Atul
= 45000 × 12 : 60000 × 9 : 90000 × 3
= 2 : 2 : 1
Atul's share

\begin{aligned} = Rs . 20000 \times \frac{1}{5} \\ = Rs . 4000 \end{aligned}

32. Rahul and Bharti are partners in a business. Rahul contributes $\frac{1}{4}$ th capital for 15 months and Bharti received $\frac{2}{3}$ of profit. For how long Bharti money was used.

A. 8 months

B. 10 months

C. 11 months

D. 17 months

Discuss

Solution:

\begin{aligned} Let the total profit be R s . Z \\ Bharti's share = \frac{2}{3} Z \\ Rahul's share = Z - \frac{2}{3} Z \\ = \frac{Z}{3} \\ Rahul:Bharti \\ = \frac{Z}{3} : \frac{2}{3} Z = 1 : 2 \\ Now let the total capital be R s X, \\ and Bharti capital was used for Y months . \\ then, Rahul capital will be \frac{1}{4} X \\ and Bharti capital will be X - \frac{1}{4} X \\ = \frac{3 X}{4} \\ \frac{\frac{1}{4} X * 15}{\frac{3}{4} X * Y} = \frac{1}{2} \\ Y = \frac{15 * 2}{3} = 10 \\ So, Bharti's money was used for 10 months \end{aligned}

33. P and Q started a business investing Rs. 85000 and Rs. 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.

A. 17 : 5

B. 17 : 3

C. 17 : 6

D. 17 : 7

Discuss

Solution:

In this type of question as time frame for both investors is equal then just get the ratio of their investments.
P : Q = 85000 : 15000
= 85 : 15
= 17 : 3

34. A, B and C enter into a partnership investing Rs 35000, Rs 45000 and Rs 55000 resp. The respective share of A,B and C in an annual profit of Rs 40500 are.

A. Rs. 11500, Rs. 13500, Rs. 16500

B. Rs. 10500, Rs. 12500, Rs. 16500

C. Rs. 10500, Rs. 13500, Rs. 15500

D. Rs. 10500, Rs. 13500, Rs. 16500

Discuss

Solution:

\begin{aligned} A : B : C \\ = 35000 : 45000 : 55000 \\ = 7 : 9 : 11 \\ Now we are having the ratio . \\ to get the share, first make total of above ratio . \\ then get each share . \\ A's Share = 40500 * \frac{7}{27} \\ = R s . 10500 \\ B's Share = 40500 * \frac{9}{27} \\ = R s . 13500 \\ C's Share = 40500 * \frac{11}{27} \\ = R s . 16500 \end{aligned}

35. Rahul, Arun and Sumit started a business. Rahul invested $\frac{1}{2}$ part, Arun $\frac{1}{3}$ part and rest of the capital was invested by Sumit. The ratio of their profits will be = ?

A. 2 : 3 : 1

B. 3 : 2 : 1

C. 2 : 3 : 6

D. 3 : 2 : 5

Discuss

Solution:

Let total capital be Rs. x

\begin{aligned} Then, \\ Rahul's share \\ = Rs . \frac{x}{2} \\ Arun's share = Rs . \frac{x}{3} \\ Sumit's share \\ = Rs . [x - (\frac{x}{2} + \frac{x}{3})] \\ = Rs . \frac{x}{6} \\ ∴ Required ratio \\ = \frac{x}{2} : \frac{x}{3} : \frac{x}{6} \\ = \frac{1}{2} : \frac{1}{3} : \frac{1}{6} \\ = 3 : 2 : 1 \end{aligned}

36. Samaira, Mahira and Kiara rented a set of DVDs at a rent of Rs. 578. If they used it for 8 hours, 12 hours and 14 hours respectively, what is Kiara's share of rent to be paid ?

A. Rs. 192

B. Rs. 204

C. Rs. 215

D. Rs. 238

Discuss

Solution:

\begin{aligned} Ratio of shares \\ = 8 : 12 : 14 \\ = 4 : 6 : 7 \\ ∴ Kiara's share \\ = Rs . (578 \times \frac{7}{17}) \\ = Rs. 238 \end{aligned}

37. P, Q and R invested Rs. 45000, Rs. 70000 and Rs. 90000 respectively to start a business. At the end of 2 years, they earned a profit of Rs.164000. What will be Q's share in the profit ?

A. Rs. 36000

B. Rs. 56000

C. Rs. 64000

D. Rs. 72000

Discuss

Solution:

\begin{aligned} ∵ P : Q : R \\ = 45000 : 70000 : 90000 \\ = 9 : 14 : 18 \\ ∴ Q's share \\ = Rs . (164000 \times \frac{14}{41}) \\ = Rs. 56000 \end{aligned}

38. A working partner gets 20% as his commission of the profit after his commission is paid. If the working partner's commission is Rs. 8000, then what is the total profit in the business ?

A. Rs. 47000

B. Rs. 45000

C. Rs. 48000

D. None of these

Discuss

Solution:

Let the total profit = Rs. k
According to the question,
Remaining profit after paying 20% working
Partner's commission = (k - 8000)

\begin{aligned} ∴ (k - 8000) \times \frac{20}{100} = 8000 \\ \Leftrightarrow k = 48000 \\ ∴ Total profit = Rs . 48000 \end{aligned}

39. We have to divided a sum of Rs. 13950 among three persons A, B and C. B must get the double of A's share and C must get Rs. 50 less than the double of B's share. The share of A will be ?

A. Rs. 1950

B. Rs. 1981.25

C. Rs. 2000

D. Rs. 2007.75

Discuss

Solution:

Lert the share of A = Rs. x
According to the question,

\begin{aligned} A : B : C \\ Capital \to x : 2 x : (4 x - 50) \\ \Rightarrow (x + 2 x + 4 x - 50) = 13950 \\ \Rightarrow 7 x - 50 = 13950 \\ \Rightarrow 7 x = 14000 \\ \Rightarrow x = 2000 \\ Share of A = Rs . 2000 \end{aligned}

40. Prakash, Sachin and Anil started a business jointly investing Rs. 11 lakh, Rs. 16.5 lakh and Rs.8.25 lakh respectively. The profit earned by them in the business at the end of 3 years was Rs. 19.5 lakh. What will be 50% of Anil's share in the profit ?

A. Rs. 2.25 lakh

B. Rs. 2.50 lakh

C. Rs. 3.75 lakh

D. Rs. 4.50 lakh

Discuss

Solution:

\begin{aligned} ∵ Ratio of shares \\ = 11 : 16.5 : 8.25 \\ = 4 : 6 : 3 \\ Anil's share \\ = Rs . (19.5 \times \frac{3}{13}) \\ = Rs. 4 .5 lakh \\ ∴ Required amount \\ = 50 % of 4 .5 lakh \\ = Rs. 2 .25 lakh \end{aligned}

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