model 11 ratio & partnership Section-Wise Topic Notes With Detailed Explanation And Example Questions

MOST IMPORTANT quantitative aptitude - 11 EXERCISES

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The following question based on profit & loss topic of quantitative aptitude

Questions : The ratio of the quantities of sugar, in which sugar costing Rs.20 per kg. and Rs.15 per kg. should be mixed so that there will be neither loss nor gain on selling the mixed sugar at the rate of Rs.16 per kg, is

(a) 1 : 2

(b) 2 : 1

(c) 4 :1

(d) 1 : 4

The correct answers to the above question in:

Answer: (d)

Let x kg of sugar costing Rs.20/ kg and y kg of sugar costing Rs.15/kg are mixed.

According to the question,

20x + 15y = 16 (x + y)

20x + 15y = 16x + 16y

20x - 16x = 16y - 15y

4x = y ∴ $x/y = 1/4$ or 1 : 4

Method 2 :

By the rule of alligation,

∴ Required ratio = 1 : 4

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Read more ratio partnership Based Quantitative Aptitude Questions and Answers

Question : 1

The ratio of cost price and selling price is 5 : 4, the loss per cent is :

a) 25%

b) 20%

c) 40%

d) 50%

Answer: (b)

According to the question

$\text"Cost price"/ \text"Selling price" = 5/4$

Selling price = $4/5$ × Cost price

Loss = Cost price - Selling price

= Cost price - $4/5$ Cost price = $1/5$ Cost price

Loss % = ${{1/5}\text"Cost price" × 100}/\text"Cost price" = 100/5 = 20%$

Method 2 : Simple Approach

Rs.1 is loss on Rs.5.

loss % = $1/5$ × 100 = 20%

Using Rule 2

If C.P > S.P., then there will be Loss

Loss = C.P. - S.P., Loss% = ${Loss × 100}/{C.P.}$

Here, C.P. = 5x, S.P. = 4x

Loss% = $\text"Loss"/ \text"C.P."$ × 100

= ${5x - 4x}/{5x}$ × 100 = 20%

Question : 2

A, B and C rent a pasture. A puts in 10 oxen for 7 months, B 12 oxen for 5 months and C 15 oxen for 3 months for grazing. If the rent of the pasture is Rs.175/-, how much must C pay as his share of rent?

a) Rs.50/-

b) Rs.45/-

c) Rs.55/-

d) Rs.60/-

Answer: (b)

Share of rent = (number of oxen × time)

A : B : C = (10 × 7) : (12 × 5) : (15 × 30)

A : B : C = 70 : 60 : 45

A : B : C = 14 : 12 : 9

C’s share of rent = $9/{14 + 12 + 9} × 175$

= $9/35 × 175$ = 45

C’s share of rent is Rs.45

Question : 3

A, B and C are partners of a company. During a particular year A received one-third of the profit, B received one-fourth of the profit and C received the remaining Rs.5,000. How much did A receive?

a) Rs.4,000

b) Rs.5,000

c) Rs.3,000

d) Rs.1,000

Answer: (a)

Let the profit be x

According to question,

$(1 - 1/3 - 1/4)x$ = Rs.5000

or $({12 - 4 - 3}/12)x$ = Rs.5000

$5/12x$ = Rs.5000

x = ${5000 × 12}/5$

= $1/3 = {5000 × 12}/{5 × 3}$ = Rs.4000

Question : 4

A invests Rs.64,000 in a business. After few months B joined him with Rs.48,000. At the end of year, the total profit was divided between them in the ratio 2 : 1. After how many months did B join?

a) 4

b) 8

c) 6

d) 7

Answer: (a)

B entered after x months.

Ratio of equivalent capitals for 1 month

= 64000 × 12 : 48000 (12 - x)

= 16 : (12 - x)

$16/{12 - x} =2/1$ ⇒ 24 - 2x = 16

2x = 8 ⇒ x = 4 months

Question : 5

A started a business with a capital of Rs.1,00,000. One year later, B joined him with a capital of Rs.2,00,000. At the end of 3 years from the start of the business, the profit earned was 84,000. The share of B in the profit exceeded the share of A by

a) Rs.12,000

b) Rs.10,000

c) Rs.14,000

d) Rs.15,000

Answer: (a)

Ratio of equivalent capitals of A and B for 1 month

= 100000 × 36 : 200000 × 24

= 36 : 48 = 3 : 4

Part of profit gained by A = $3/7$

Part of profit gained by B = $4/7$

Required difference

$(4/7 - 3/7) × 84000$ = Rs.12000

Question : 6

A milkman makes 20% profit by selling milk mixed with water at Rs.9 per litre. If the cost price of 1 litre pure milk is Rs.10, then the ratio of milk and water in the said mixture is

a) 4 : 1

b) 3 : 1

c) 3 : 2

d) 4 : 3

Answer: (b)

Let Milk : Water = K : 1

S.P. = (K + 1) × 9

C.P. = 10K; Gain = 9 - K

Gain % = ${9 - K}/{10K} × 100$

${9 - K}/{10K} × 100$ = 20

90 - 10K = 20K

30K = 90 ⇒ K = 3

Ratio = 3 : 1

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