model 11 ratio & partnership Practice Questions Answers Test with Solutions & More Shortcuts

Question : 16 [SSC CGL Prelim 2008]

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 : 17 [SSC CHSL 2013]

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 : 18 [SSC DEO 2008]

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

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

Question : 19 [SSC CGL Prelim 2002]

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 : 20 [SSC CGL Prelim 2000]

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

IMPORTANT quantitative aptitude EXERCISES

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