Practice | Hashtable

content Computer Science Arithmetic Aptitude Data Interpretation Logical Reasoning Verbal Reasoning Non-Verbal Reasoning

About About Privacy Policy

Hashtable

Home
Practice
PYQ
Mock Test
Register Free

Home Practice PYQ Mock Test Register Free

Home > Practice > Arithmetic Aptitude > Partnership > Miscellaneous

91. A and B enter into a partnership with Rs. 50000 and Rs. 60000 respectively. C joins them after x months, contributing Rs. 70000 and B leaves x months before the end of the year. If they share the profit in the ratio of 20 : 18 : 21, then the value of x is = ?

A. 3

B. 6

C. 8

D. 9

Discuss

Solution:

Clearly, A invested his capital for 12 months
while each one of B and C invested his capital for (12 - x) months
Ratio of profits os A, B, C

= (50000 \times 12)

[60000 \times (12 - x)]

[70000 \times (12 - x)]

\begin{aligned} = 60 : 6 (12 - x) : 7 (12 - x) \\ But ratio of profits \\ = 20 : 18 : 21 \\ = 60 : 54 : 63 \end{aligned}

∴ 60 : (72 - 6 x) : (84 - 7 x)

60

54

63

\begin{aligned} So, 72 - 6 x = 54 \\ \Rightarrow 6 x = 18 \\ \Rightarrow x = 3 \end{aligned}

92. Two friends P and Q started a business investing in the ratio 5 : 6. R joined them after six months investing an amount equal to that of Q's. At the end of the year, 20% profit was earned which was equal to Rs. 98000. What was the amount invested by R?

A. Rs. 105000

B. Rs. 175000

C. Rs. 210000

D. Data inadequate

Discuss

Solution:

Let the total investment be Rs. z
Then,

\begin{aligned} 20 % of z = 98000 \\ \Leftrightarrow z = (\frac{98000 \times 100}{20}) \\ \Leftrightarrow z = 490000 \end{aligned}

Let the capital of P, Q and R be
Rs. 5x, Rs. 6x and Rs. 6x respectively
Then,

\Leftrightarrow (5 x \times 12)

(6 x \times 12)

(6 x \times 6)

490000 \times 12

\begin{aligned} \Leftrightarrow 168 x = 490000 \times 12 \\ \Leftrightarrow x = (\frac{490000 \times 12}{168}) \\ \Leftrightarrow x = 35000 \\ ∴ R's investment \\ = Rs . 6 x \\ = Rs . (6 \times 35000) \\ = Rs . 210000 \end{aligned}

93. A, B and C invested their capitals in the ratio 3 : 4 : 6. However their share of profit are equal. The duration of their investments must be in the ratio ?

A. 4 : 3 : 2

B. 6 : 4 : 3

C. 3 : 4 : 6

D. 1 : 1 : 1

Discuss

Solution:

Let their investments be Rs. 3x for p months
Rs. 4x for q months and Rs. 6x for r months respectively
Then,

\begin{aligned} 3 x p : 4 x q : 6 x r = 1 : 1 : 1 \\ \Rightarrow 3 p : 4 q : 6 r = 1 : 1 : 1 \\ So, 3 p = 4 q \\ \Leftrightarrow q = \frac{3 p}{4} \\ And, 4 q = 6 r \\ \Leftrightarrow r = \frac{2 q}{3} = (\frac{2}{3} \times \frac{3}{4} p) = \frac{p}{2} \\ ∴ p : q : r \\ = p : \frac{3 p}{4} : \frac{p}{2} \\ = 4 : 3 : 2 \end{aligned}

94. Swati and Rajni enter into a partnership with their capitals in the ratio 5 : 6. At the end of 7 months Swati withdraws her capital. If they receive the profit in the ratio of 5 : 9, find how long was Rajni's capital used ?

A. 10 months

B. 12 months

C. 14 months

D. None of these

Discuss

Solution:

Suppose,
Swati invested Rs. 5x for 7 months
And
Rajni invested Rs. 6x for y months
Then,

\begin{aligned} \Rightarrow \frac{5 x \times 7}{6 x \times y} = \frac{5}{9} \\ \Rightarrow 30 y = 315 \\ \Rightarrow y = 10 \frac{1}{2} \end{aligned}

Hence, Rajni's capital was used for

10 \frac{1}{2}

months

95. X and Y are partners in a business. X contributed $\frac{1}{3}$ of the capital for 9 months and Y received $\frac{2}{5}$ of the profit. For how long was Y's money used in the business ?

A. 2 months

B. 3 months

C. 4 months

D. 5 months

Discuss

Solution:

\begin{aligned} Let  the total profit be Rs . z \\ Then, \\ Y's share = Rs . \frac{2 z}{5} \\ X's share = Rs . (z - \frac{2 z}{5}) \\ = Rs . \frac{3 z}{5} \\ ∴ X : Y \\ = \frac{3 z}{5} : \frac{2 z}{5} \\ = 3 : 2 \end{aligned}

Let the total capital be Rs. x and
Suppose Y's money was used for y months
Then,

\begin{aligned} \Rightarrow \frac{\frac{1}{3} x \times 9}{\frac{2}{3} x \times y} = \frac{3}{2} \\ \Rightarrow 18 x = 6 x y \\ \Rightarrow y = 3 \end{aligned}

Hence, Y's money was used for 3 months.

96. M, P and Q together started a business. M invested Rs. 6500 for 6 months, P invested Rs. 8400 for 5 months and Q invested Rs. 10000 for 3 months. M is working member for which he gets 5% of total profit extra. If the total gain is Rs. 7400, then Q's share is ?

A. Rs. 1900

B. Rs. 2100

C. Rs. 3200

D. Data are incomplete

Discuss

Solution:

	M	:	P	:	Q
Capital →	6500	:	8400	:	10000
	65	:	84	:	100
Time →	×6	:	×5	:	×3
	390	:	420	:	300
Profit →	13	:	14	:	10

M's extra share on work in partner

\begin{aligned} = Rs .7400 \times \frac{5}{100} \\ = Rs .370 \\ Remaining profit \\ = Rs . (7400 - 370) \\ = Rs . 7030 \end{aligned}

According to the question,
(13 + 14 + 10) units = Rs. 7030

\begin{aligned} 37 units = Rs . 7030 \\ 1 unit = Rs . \frac{7030}{37} \\ Profit of Q = 10 units \\ = Rs . \frac{7030}{37} \times 10 \\ = Rs . 1900 \end{aligned}

97. A started a business by investing Rs. 50000. After 6 months B joined her by investing Rs. 75000. After its 6 months C joined with Rs. 125000. What is the ratio of profit share after 2 year among A, B and C ?

A. 4 : 5 : 6

B. 8 : 9 : 10

C. 8 : 9 : 12

D. 4 : 5 : 8

Discuss

Solution:

	A	:	B	:	C
Capital →	50000	:	75000	:	125000
Time(year) →	2		$\frac{3}{2}$		1
Profit →	100	:	$\frac{75 \times 3}{2}$	:	125
	8	:	9	:	10

∴ Required ratio of profit = 8 : 9 : 10

98. A and B started a business with initial investments in the respective ratio of 18 : 7. After 4 months from the start of the business, A invested Rs. 2000 more and B invested Rs. 7000 more. At the end of one year, if the profit was distributed among them in the ratio of 2 : 1 respectively, what was the total initial investment with which A and B started the business ?

A. Rs. 50000

B. Rs. 25000

C. Rs. 150000

D. Rs. 75000

Discuss

Solution:

Let the initial investment of A and B is 18x and 7x
After 4 months from the start of business,
A invest Rs. 2000 more for each eight months.
Then total investment of A

\begin{aligned} = 18 x \times 4 + (18 x + 2000) \times 8 \\ = 72 x + 144 x + 16000 \\ = 216 x + 16000 \end{aligned}

After 4 months, from the start of business,
B invest Rs. 7000 more for each eight months.
Total investment by B

\begin{aligned} = 7 x \times 4 + (7 x + 7000) \times 8 \\ = 28 x + 56 x + 56000 \\ = 84 x + 56000 \end{aligned}

According to the question,

\Rightarrow \frac{216 x + 16000}{84 x + 56000} = \frac{2}{1}

⇒ 216x + 16000 = 168x + 112000
⇒ 216x - 168x = 112000 - 16000
⇒ 48x = 96000
⇒ x = 2000
Total initial investment of A and B
= (18 + 7) × 2000
= Rs. 50000

99. Anil, Kamal and Vini invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Anil left after 6 months. If after 8 months, there was a gain of Rs. 4005, then what will be the share of Kamal ?

A. Rs. 800

B. Rs. 890

C. Rs. 500

D. Rs. 900

Discuss

Solution:

Ratio of profit of Anil : Kamal : Vini
(8000 × 6) : (4000 × 8) : (8000 × 8)
= 48000 : 32000 : 64000
= 48 : 32 : 64
= 3 : 2 : 4

\begin{aligned} ∴ Kamal's share \\ = Rs . (4005 \times \frac{2}{9}) \\ = Rs . 890 \end{aligned}

100. A starts a business by investing Rs. 28000. After 2 months, B joins with Rs. 20000 and after another 2 months C joins with Rs. 18000. At the end of 10 months from the start of the business, if B withdraws Rs. 2000 and C withdraws Rs. 2000, in what ratio should the profit be distributed among A, B and C at the end of the year ?

A. 12 : 7 : 5

B. 12 : 9 : 5

C. 12 : 6 : 3

D. 14 : 7 : 5

Discuss

Solution:

A invests money for 12 months
B invests money for 10 months
C invests money for 8 months
Ratio of profit of A to B to C
= 28000 × 12 : 20000 × 8 + 18000 × 2 : 18000 × 6 + 16000 × 2
= 28 × 12 × 1000 : (160 + 36) × 1000 : (108 + 32) × 1000
= 28 × 12 : 160 + 36 : 108 + 32
= 336 : 196 : 140
= 12 : 7 : 5

1 2 3 4 5 6 7 8 9 10

Sign up for our newsletter

Are you passionate about opportunities in the realm of Computer Science within the government sector? Don't miss out on crucial updates, job openings, and career prospects tailored specifically straight to your inbox.

Email address

By subscribing, you agree with our Terms of Service and Privacy Policy.

Resources

Practice PYQ Mock Test

Company

About us Contact us Privacy policy Terms of service

Hashtable