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)
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)
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)
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)
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)
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)
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)
$b = a × 200/100 = 2a$
$b/a = 2 ⇒ b/a - 1 = 2 - 1$
${b - a}/a = 1 ⇒ {b - a}/a × 100 = 100$
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)
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)
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)
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