Practice Ratio partnership - quantitative aptitude Online Quiz (set-1) For All Competitive Exams

Q-1)   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)

(b)

(c)

(d)

Explanation:

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


Q-2)   If the cost price and selling price of an article are in the ratio 10 : 11, then the percentage of profit is :

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

Let Cost price = 10x

Selling price = 11x

Gain per cent = ${11x - 10x}/{10x} × 100$

= $x/{10x} × 100 = 10%$


Q-3)   Nita blends two varieties of tea— one costing Rs.180 per kg and another costing Rs.200 per kg in the ratio 5 : 3. If she sells the blended variety at Rs.210 per kg, then her gain percent is

(a)

(b)

(c)

(d)

Explanation:

Gain per cent

= ${210 × (5 + 3) -[180 × 5 + 200 × 3]}/{180 × 5 + 200 × 3}$ × 100

= ${1680 - 1500}/1500 × 100$

= $180/1500 × 100$ = 12%


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

(a)

(b)

(c)

(d)

Explanation:

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%


Q-5)   The ratio of cost price and selling price of an article is 8 : 9. The profit per cent is

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

If S.P > C.P. then there will be profit

Profit = S.P. - C.P.

Profit% = ${\text"Profit" × 100}/{\text"C.P."}$

Let the CP = 8x and SP = 9x

Profit = (9x - 8x) = x

Profit % = $x/{8x} × 100 = 25/2 =12.5%$


Q-6)   The ratio of the C.P. and S.P. of an article is 20 : 21. What is the gain per cent ?

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

If S.P > C.P. then there will be profit

Profit = S.P. - C.P.

Profit% = ${\text"Profit" × 100}/{\text"C.P."}$

Tricky Approach

Gain% = ${(21 - 20)}/20 × 100 = 1/20 × 100$ = 5%


Q-7)   The cost price : selling price of an article is a : b. If b is 200% of a then the percentage of profit on cost price is

(a)

(b)

(c)

(d)

Explanation:

$b = a × 200/100 = 2a$

$b/a = 2 ⇒ b/a - 1 = 2 - 1$

${b - a}/a = 1 ⇒ {b - a}/a × 100 = 100$

Gain per cent = 100%


Q-8)   In what ratio must a grocer mix tea at Rs.60 a kg, and Rs.65 a kg, so that by selling the mixture at Rs.68.20 a kg, he may gain 10%?

(a)

(b)

(c)

(d)

Explanation:

S.P. of 1 kg mixture = Rs.68.20, Gain = 10%

C.P. of 1 kg mixture = Rs.$(68.20 × 100/110)$ = Rs.62

By the rule of alligation,

∴ Required ratio = 3 : 2


Q-9)   In what ratio Darjeeling Tea costing Rs.320 per kg be mixed with Assam Tea costing Rs.250 per kg so that there is a gain of 20% by selling the mixture at Rs.324 per kg ?

(a)

(b)

(c)

(d)

Explanation:

CP of the mixture = ${324 × 100}/120$ = Rs.270

∴ Required ratio = 2 : 5


Q-10)   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)

(b)

(c)

(d)

Explanation:

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