Successive Selling MCQ Quiz - Objective Question with Answer for Successive Selling - Download Free PDF

Given:

Selling Price 1 (SP1) = ₹3,437 (results in gain)

Selling Price 2 (SP2) = ₹3,338 (results in loss)

Gain (G) = 75% more than Loss (L)

Required Gain = 50%

Formula used:

Gain = Selling Price - Cost Price (SP - CP)

Loss = Cost Price - Selling Price (CP - SP)

Required SP = CP ×

Calculations:

Let CP be the Cost Price.

Gain (G) = SP1 - CP = 3437 - CP

Loss (L) = CP - SP2 = CP - 3338

Given, Gain is 75% more than Loss:

G = L + 0.75L

⇒ G = 1.75L

Substitute the expressions for G and L:

3437 - CP = 1.75 × (CP - 3338)

⇒ 3437 - CP = 1.75CP - 1.75 × 3338

⇒ 3437 - CP = 1.75CP - 5841.5

⇒ 3437 + 5841.5 = 1.75CP + CP

⇒ 9278.5 = 2.75CP

⇒ CP =

⇒ CP = ₹3374

Now, to gain 50%, the new Selling Price (SP_new) will be:

SP_new = CP ×

⇒ SP_new = 3374 × (1 + 0.5)

⇒ SP_new = 3374 × 1.5

⇒ SP_new = ₹5061

∴ The selling price to gain 50% is ₹5,061.

Given:

Cost Price (CP) of 6 lemons = ₹1

Required Gain = 100%

Formula used:

Selling Price (SP) = CP + Gain

Gain = Percentage Gain of CP

If gain is 100%, then SP = CP × = CP × 2

Calculations:

CP of 6 lemons = ₹1

To gain 100%, the Selling Price (SP) of 6 lemons must be:

SP of 6 lemons = CP of 6 lemons + 100% of CP of 6 lemons

⇒ SP of 6 lemons = ₹1 + 100% of ₹1

⇒ SP of 6 lemons = ₹1 + ₹1

⇒ SP of 6 lemons = ₹2

This means the vendor must sell 6 lemons for ₹2 to gain 100%.

We need to find how many lemons he must sell for ₹1.

If 6 lemons are sold for ₹2,

Then, for ₹1, the number of lemons sold =

⇒ Number of lemons = 3

∴ He must sell 3 lemons for ₹1 to gain 100%.

Given:

Selling price of bed = 2 × Initial selling price.

Profit = 10 × Initial profit.

Formula Used:

Profit Percentage = (Profit / Cost Price) × 100

Let Initial Cost Price = C, Initial Profit = P, and Initial Selling Price = S.

Relation between Selling Price, Profit, and Cost Price: S = C + P

Calculation:

New Selling Price = 2 × S

New Profit = 10 × P

⇒ S = C + P

⇒ 2 × S = C + 10 × P

Substitute S = C + P in 2 × S:

⇒ 2 × (C + P) = C + 10 × P

⇒ 2C + 2P = C + 10P

⇒ 2C - C = 10P - 2P

⇒ C = 8P

Initial Profit Percentage = (P / C) × 100

⇒ Initial Profit Percentage = (P / 8P) × 100

⇒ Initial Profit Percentage = (1 / 8) × 100

⇒ Initial Profit Percentage = 12.5%

The initial profit percentage is 12.5%.

Calculation:

Let cost price of the item be Rs. x

According to the question

(x – 440) = (1000 – x) × 60/100

⇒ (x – 440) = (1000 – x) × 3/5

⇒ 5x – 2200 = 3000 – 3x

⇒ 5x + 3x = 3000 + 2200

⇒ 8x = 5200

⇒ x = 5200/8

⇒ x = 650

∴ The correct answer is option (1).

Shortcut Trick

Given:

Total cost of potatoes and onions: Rs. 25,000

Gain on potatoes: 30%,  Loss on onions: 10%, and Overall gain: 20%

Calculation:

Let P be the buying price of potatoes and O be the buying price of onions. 

⇒ P + O = Rs. 25,000 →(1)

According to the question,

The overall gain of 20% on total cost,

⇒ SP = 25000 ×  = Rs. 30000

The gain on selling potatoes is 30%, SP of potatoes= 1.3P

The loss on selling onions is 10%, SP of onions = 0.9O

Now, the selling prices of potatoes and onions add up to the total selling price,

⇒ 1.3P + 0.9O = 30,000

⇒ 1.3P + 0.9(25,000 - P) = 30,000    [From Eqn (1)]

⇒ 1.3P + 22,500 - 0.9P = 30,000

⇒ 0.4P = 7,500

⇒ P =  = Rs. 18750

∴ Option (2) is the correct answer.

Shortcut Trick 

Given :

A TV  set selling price in Delhi = Rs. X 

The discount is given on TV set in Chandigarh = 20%

Profit % = 100/7% = %

Transportation cost = Rs. 600

Formula Used:

Selling price = Cost Price × (100 + P%)/100

Calculation:

CP = 80% of X = 0.8X

According to the question

⇒ X = 

⇒ X =  

⇒ 100X =  

⇒ 700X = (0.8X + 600)(800)

⇒ 700X = 640X + 480000

⇒ 60X = 480000

⇒ X = 8000

∴ The value of X is Rs.8000

⇒ Selling Price of TV in Chandigarh = X – 20% of X = Rs. 0.8X

⇒ Total cost price of TV in Delhi = 0.8X + 600

⇒ Selling Price = Rs. X

⇒ Profit% = {(X – 0.8X – 600)/(0.8X + 600)} × 100

⇒ 100/7 = {(0.2X – 600) / (0.8x + 600)} × 100

⇒ 0.8X + 600 = 1.4X – 4200

⇒ X = 8000

Shortcut Trick

Fruits bought at 15 for Rs. 140

Equal quantity of bought at 10 for Rs. 120

Fruits sold at Rs. 132/dozen

Let, the total quantity of fruits = 30

               15 for Rs. 140            10 for Rs. 120          Total

CP              Rs. 140                        Rs. 180             Rs. 320

SP              Rs. 165                        Rs. 165             Rs. 330

Profit percent = (330 - 320)/320 × 100  = %

∴ The required profit percent is  %.

Alternate Method

Given:

Fruits at 15 for Rs. 140 = Fruits at 10 for Rs. 120

Fruits sold at Rs. 132/dozen

Formula used:

Profit > Loss 

Profit = SP - CP 

Profit percent = Profit/CP × 100 

Calculation:

Let, Total fruit brought

⇒ LCM (10 and 15) = 30

So, CP of 30 fruits at the rate of 15 for Rs. 140

⇒ 140/15 × 30 = Rs. 280

Similarly, CP of 30 fruits at 10 for Rs. 120,

⇒ 120/10 × 30 = Rs. 360

So, Total CP of 60 fruits = 280 + 360 = Rs. 640

Now,

⇒ SP of 12 fruits = Rs. 132

⇒ SP of 1 fruit = Rs. 11

⇒ SP of 60 fruits = Rs. 11 × 60 = Rs. 660

So, Profit = SP - CP = Rs.660 - Rs. 640 

⇒ Rs. 20 

Profit percent = 20/640 × 100 = 

∴ The required profit percent is  %.

GIVEN:

SP = Rs. 1540 when loss = 30%

CONCEPT:
Basic profit and loss concept.

FORMULA USED:

SP = CP × (1 - Loss %/100)

SP = CP × (1 + Profit %/100)

CALCULATION:

Cost price of TV = 1540/(1 - 30/100)

= 1540/0.7 = Rs. 2200

Hence,

Selling price when profit is 30% = 2200 × (1 + 30/100) = Rs. 2860

Calculation:

Let the cost price be Rs. y

When he had a profit,

Selling price = cost price + profit % of cost price

⇒ y + 25% × y = 1.25y

When he had a loss,

Selling price = cost price – loss% of cost price

⇒ y – 25% × y = 0.75y

According to the question,

⇒ 1.25y – 0.75y = 40

⇒ 0.50y = 40

⇒ y = 80

∴ Initial selling price = 1.25y = 1.25 × 80 = Rs.100

Alternate MethodCalculation:

Taking profit percentage as positive and the loss percentage as negative.

⇒ 25% - (-25%) = 40

⇒ 50% = 40

⇒ 1 = 80

S.P = 1.25 = 1.25 × 80 = 100

∴ The selling price is Rs.100.

Given,

Selling price of book = Rs. 575

Let cost price of book be Rs.a.

Concept Used:

Profit = S.P - C.P

Loss = C.P - S.P

Calculation:

⇒ Profit = 575 - a

Given,

Selling price of book = Rs. 385

⇒ Loss = a - 385

Then,

⇒ 575 - a = a - 385

⇒ 2a = 960

⇒ a = 480

∴ cost price of a book is Rs. 480

Given:

P sells an article to Q at a loss of 5%

Q sells that article to R at a loss of 20%

R pays ₹ 2812 for the article

Concept:

P sells the article to Q. Therefore Q's Cost Price will be P's Selling Price and Q sells the article to R. Therefore R's Cost Price will be Q's Selling Price

Calculation:

R pays ₹ 2812 for the article

∴ R's Cost Price = 2812

Q's Selling Price = R's Cost Price = 2812

⇒ Q's Cost Price = 2812 × (100/80) = 3515   (∵ 20% Loss)

P's Selling Price = Q's Cost Price = 3515

⇒ P's Cost Price = 3515 × (100/95) = 3700   (∵ 5% Loss)

∴  The cost price for P = ₹3700

Let the cost price be Rs. x

⇒ Loss = x/7

⇒ Selling price = x – (x/7)

⇒ 144 = 6x/7

⇒ x = 168

⇒ New selling price = Rs. 189

⇒ Gain % = {(189 – 168)/168} × 100 = 12.5%

Given:

Selling price of each articles = Rs. 10591

Gain = 19%

Loss = 11%

Calculation:

SP of each articles = Rs. 10591

CP of first article = Rs. (10591 × 100/119)

⇒Rs. 8900

CP of second article = Rs. (10591 × 100/89)

⇒ 11900

Total SP of both the article = 10591 × 2 = 21182

Total CP of both the article = 8900 + 11900 = 20800

Total Gain = 21182 – 20800 = 382

Gain percentage = (382/20800 × 100)

⇒ 1.83%

∴ His overall Profit percentage is 1.8%