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Given:

Total amount = Rs. 1900

A's share = \(1 \frac 1 2\) times of B's

And B's share = \(1 \frac 1 2\) times of C's

Formula used:

If the ratio of A and B = x : y

And the ratio of B and C = p : q

Then the ratio of A, B and C = xp : yp : yq

Calculation: 

A's share = \(1 \frac 1 2\) times of B's

⇒ A's share = 3/2 of B's share

⇒ A/B = 3/2

The ratio of A and B is 3 : 2      ----(i)

B's share = \(1 \frac 1 2\) times of C's share

⇒ B's share = 3/2 of C's share

⇒ B/C = 3/2

The ratio of B and C is 3 : 2      ----(ii)

From equation (i) and (ii), we get

The ratio of share between A, B and C = 3 × 3 : 2 × 3 : 2 × 2

⇒ 9 : 6 : 4

Let the amount of A, B and C be 9x, 6x and 4x respectively

Then, total amount = 9x + 6x + 4x

⇒ 19x

According to the question, the total amount = Rs. 1900

⇒ 19x = 1900

⇒ x = 1900/19

⇒ x = Rs. 100

Now, the share of C's = 4x

⇒ 4 × 100

⇒ Rs. 400

∴ The share of C's is Rs. 400.

Given:

The total amount = 6,045

A's share reduced = Rs.10

B's share reduced = Rs. 15

C's share reduced = Rs. 20

The ratio of their shares after redution = 5 : 4 : 3

Calculations:

Let share of A, B, and C after reduction certain amount be 5x, 4x, 3x

A's original amount = (5x + 10)

B's original amount = (4x + 15)

C's original amount = (3x + 20)

Total amount = 5x + 10 + 4x + 15+ 3x + 20

⇒ 12x + 45 = 6045

⇒ 12x + 45 = 6045

⇒ 12x = 6000

⇒ x = 500

B share is = 4x + 15 

⇒ 4 × 500 +15 = 2015

∴ B share is 2015

Given:

Total money = Rs.6060

Calculation:

Let amount of money A, B and C has after reduction be Rs.5a, Rs.7a and Rs.8a respectively.

⇒ (5a + 15) + (7a + 20) + (8a + 25) = 6060

⇒ a = 300

New share of C = Rs.2400

∴ Original share of C = 2400 + 25 = Rs.2425

Given:

Rs. 20,400 has to be divided between A, B, and C so that A gets (2/3)rd of what B gets and B gets (1/4)th of what C gets.

Calculations: 

According to the question,

A = (2/3)B, B = (1/4)C

So, A ∶ B ∶ C = (2/3)B ∶ B ∶ (4)B = 2 ∶ 3 ∶ 12

Let A, B, and C be 2x, 3x and 12x respectively.

According to the question 

⇒ 2x + 3x + 12x = 20400

⇒ 17x = 20400

⇒ x = 1200

C's share = 1200 × 12 = 14400

A's share = 1200 × 2 = 2400

Difference between C and A = 14400 – 2400 = Rs. 12000

∴ C gets Rs. 12000 more than A.

Given: 

2.1, 3.5, 5.4

Formula Used: 

If a : b :: c : d

then a × d = b × c 

Calculation: 

a : b :: c : d,

⇒ 2.1 : 3.5 :: 5.4 : d

⇒ 2.1 × d = 3.5 × 5.4 

⇒ d = 9.0 

∴ The required answer is 9.0 

Given:

Total amount to be divide = Rs.270

Calculations:

Let the amount of C's portion be 'x'

B's portion = 3/4 of c's portion

⇒ 3x/4

A's portion = 2/3 of B's portion 

⇒ (2/3) × 3x/4 = x/2

Total amount = A + B + C

⇒ 270 = x + 3x/4 + x/2

⇒ 270 = (4x + 3x + 2x)/4

⇒ 270 = 9x/4

⇒ 270 × 4  = 9x 

⇒ 30 × 4 = x

⇒ x = 120

A's portion = x/2

⇒ 120/2 = 60

B's portion = 3x/4

⇒ 3 × 120/4 = 90

∴ The required portion of money A, B, and C is 60, 90, and 120 respectively

Given :

let x be the fourth proportional of  3,7 and 15 

then 3 : 7 :: 15 : x 

Concept Used:

If  a : b :: c : d

then ad = bc

d = bc/a

Calculation:

3/7 = 15/x

⇒ x = (15 × 7) / 3 

⇒ x = 35

∴ Fourth proportional of 3, 7 and 15 is 35

Given:

378, 546, and 306 are in proportion.

Concept used:

If a, b, c, and d are in proportion

then (a/b) = (c/d)

Calculations:

Let the fourth proportional be x.

Then (378/546) = (306/x)

⇒ x = (546 × 306)/378

⇒ x = 442

∴ The fourth proportional is 442.

Given:

First number = 225

Second number = 270

Third number = 145

Concept used:

1.) An equality of two ratios is called as proportion i.e. a/b = c/d, then we can say that a, b, c and d are in proportion.

When a, b, c and d are in proportion, it can be written as

a ∶ b ∶∶ c ∶ d

Where a and d are Extremes and b and c are Means

Product of Extremes would be the same as the product of Means

ad = bc

2.) Fourth proportional (x be the fourth proportional to a, b and c)

a ∶ b ∶∶ c ∶ x

xa = bc

Calculations:

Let fourth proportional be x

According to definition of fourth proportional

225 ∶ 270 ∶∶ 145 ∶ x

⇒ 225x = 270 × 145

⇒ x = (270 × 145) /225

⇒ x = 174

Given:

Ramesh's investment = Rs. 40000

Kevin's investment = Rs. 20000

Total profit at the end of the year = Rs. 10000

Ramesh's time period of investment = 12 months

Kevin's time period of investment = 6 months

Formula used:

(Ramesh's profit) ∶ (Kevin's profit) = (Ramesh's capital × Time period of investment) ∶ (Kevin's capital × Time period of investment)

Calculations:

Ratio of their profit = (40000 × 12) ∶ (20000 × 6)

⇒ 480000 ∶ 120000

⇒ 4 ∶ 1

Ramesh's profit = 4x

Kevin's profit = x

Total profit = 4x + x

⇒ 5x = 10000

⇒ x = Rs. 2000 

∴ The share of Kevin in the total profit is Rs. 2000

Given:

The ratio of the present age of Riti and her father = 6 : 13.

After 4 years

the age of her father = double of Riti's age.

Calculation:

The ratio of the present age of Riti and her father is 6 : 13

Let, her present age is 6x and that of her father is 13x

After 4 years her age will be (6x + 4)

After 4 years her father’s age will be (13x + 4)

Accordingly,

(13x + 4) = 2 × (6x + 4)

⇒ 13x + 4 = 12x + 8

⇒ 13x – 12x = 8 – 4

⇒ x = 4

Riti’s present age is (6 × 4) = 24 years

And her father’s present age is (13 × 4) = 52

At the time of her birth her father’s age was (52 – 24) = 28 years

∴ The age of her father was 28 years at the time of her birth.

Given:

Total profit of Rs. 900

The ratio of Aditi ∶ Ashok = 3 ∶ 2

The ratio of Ashok and Sneha = 4 ∶ 5

Concept used:

Ratio concept used.

Calculation:

Aditi ∶ Ashok  = 3 ∶ 2

Ashok and Sneha = 4 ∶ 5

Multiply the ratio of Aditi and Ashok by 2, we get

Aditi ∶ Ashok  = 6 ∶ 4

⇒ Aditi : Ashok : Sneha = 6 ∶ 4 ∶ 5

Let the profit of Aditi , Ashok and Sneha  be 6x , 4x and 5x .

total profit  = Rs. 900

⇒ 6x + 4x + 5x = 900

⇒ 15x = 900

⇒ x = 60

So, Aditi’s profit = 6x = 6 × 60 = Rs. 360.

∴ Aditi’s profit is Rs. 360.

Given:

A and B started a partnership business investing in the ratio of 7 ∶ 10. C joined them after 6 months with an amount equal to (4/5)th of B.

C's profit = Rs. 42,000

Concept used:

Divide the total profit according to investment ratio.

Calculations:

Let A’s investment be Rs. 7x and B’s investment be Rs. 10x

Then C’s investment = Rs. 10x × (4/5) = Rs. 8x

Ratio of their equivalent capitals for 1 month = (7x × 12) ∶ (10x × 12) ∶ (8x × 6)

⇒ 84 ∶ 120 ∶ 48 = 7 ∶ 10 ∶ 4

Let the ratio be 7k, 10k and 4k and total profit be y.

Then C's share = [4k/(21k)] × y

But according to question (4y/21) = 42,000

⇒ y = Rs. 220500

∴ Their profit at the end of the year was Rs. 2,20,500.

Given:

Final amount = P + interest ( 5 instalment ) = 9361

Time period is 5 years

Rate % = 5%

Formula used :

\(instalment = \frac{{100 \times amount}}{{\begin{array}{*{20}{c}} {100 \times n + \;R \times \frac{{n\left( {n - 1} \right)}}{2}}\\ {} \end{array}}}\)

\(\begin{array}{l} Calculation:\\ instalment = \frac{{100 \times 9361}}{{100 \times 5 + 5 \times \frac{{5\left( {5 - 1} \right)}}{2}}} = 1702 \end{array}\)

Given:

Distance between trains = 100 km

Speed of faster = 50 km/hr

Speed of slower train = x km/hr

Time taken to overtake = x/6 hour

Concept used:

When A and B travel in the same direction = Relative speed becomes A – B (i.e. Relative speed is difference of their individual speed when they travel in same direction)

When A and B travel towards each other = Relative speed becomes A + B (i.e. Relative speed is sum of their individual speed when they travel towards each other)

Time = Distance/Speed

Calculation:

Relative speed = (50 – x) km/hr

Time taken = Distance between them/Relative speed

⇒ x/6 = 100/(50 – x)

⇒ x × (50 – x) = 6 × 100

⇒ 50x – x² = 600

⇒ x² – 50x + 600 = 0

⇒ x² – 30x – 20x + 600 = 0

⇒ x × (x – 30) – 20 × (x – 30) = 0

⇒ (x - 20) × (x - 30) = 0

⇒ x = 30 and x = 20

There are two values of x which satisfy the given conditions.

∴ The speed of slower train can be 30 km/hr or 20 km/hr    

Given:

Initial Selling Price of the article = Rs. 1500

Initial Discount on the Selling Price = 10%

Initial Profit on selling the article = 8%

Final Profit = 12%

Formulae Used:

Selling Price = [(100 + Profit%) / 100] × Cost Price

New Selling Price (SP), when discount on the Old Selling Price is given:

New SP = [(100 - Discount%) / 100] × Old SP

Calculation:

∵ 10% initial discount on the initial SP is given,

New SP = [(100 - 10)/100] × 1500

⇒ New SP = Rs. 1350

On this new SP, the profit earned is 8%, we obtain the CP as:

1350 = [(100 + 8) / 100] × CP

⇒ CP = 135000/108

⇒ CP = Rs. 1250

Now, when the article is sold at a profit of 12%, we obtain the final SP as:

Final SP = [(100 + 12) / 100] × 1250

⇒ Final SP = Rs. 1400

∴ The required Selling Price (SP) is Rs.1400

Given:

Marked price = 35% above the cost price

Profit% = 20%

Formula used:

Discount% = (Discount/M.P) × 100%

Calculation:

Let the cost price be Rs. 100x

Marked price = Rs. 100x × (135/100)

⇒ Rs. 135x

Selling price = Rs. 100x × (120/100)

⇒ Rs. 120x

Discount = Rs. (135x – 120x)

⇒ Rs. 15x

Discount% = (15x/135x) × 100%

⇒ 100/9%

∴ The discount% offered on the marked price is 100/9%

Given:

Profit earned by Shruti = 25%

Loss suffered by Ankit = 20%

Cost price of laptop for Shruti = Rs. 80,000

Calculation:

Selling price of laptop for Ankita = 80,000 + 25% of 80,000

⇒ Rs. 1,00,000

Cost price of laptop for Ankita = Rs. 1,00,000

Selling price of laptop for Ankita = Rs.1,00,000 – 20% of 1,00,000

⇒ Rs. 80,000

Hence, cost price of laptop for Anita is Rs. 80,000.

Given :

Selling price of two articles is Rs. 270

Formula used :

Profit = selling price - cost price 

 Calculations :

Selling price of 2 articles = 2 × 270 = 540 rupees 

Profit = selling price of two articles - Cost price of 2 articles 

Cost price = 540 - 2 × cost price         (profit = cost price of one article)

3 cost price = 540

Cost price = 540/3 = 180 rupees 

Profit % = (540 - 360)/(360) × 100 

⇒ 50% 

∴ The required answer is Rs. 180 and 50%

Given :

Bella sold a painting worth $1450 at 10% profit 

Teddy sold it to Benny at 10% loss 

Formula used :

Selling price = Cost price + profit on cost price (at profit)

Selling price = cost price - loss on cost price  (at loss)

Calculations :

Selling price for Bella(Cost price for Teddy) = 1450 + 10% of 1450 

⇒ 1450 + 145 = $1595 

Selling price for Teddy(Cost price for Benny) = 1595 - 10% of 1595 

⇒ 1595 - 159.5 = $1435.5 

Now loss or profit percent if Bella had sold his painting at $1435.5 instead of $1450 

So, 

Loss per cent = (cost price - selling price)/Cost price) × 100 

⇒ (1450 - 1435.5)/1450) × 100 

⇒ 1% 

∴ Bella would faced a loss of 1% if he sold it for Selling price of Teddy 

Given

selling price of 5 articles is equals to the cost price of 3 articles

Formula used

Profit % = \(\frac{{SP - CP}}{{CP}} × 100\)

Calculation 

SP of 5 article = CP of 3 article

⇒ 5 SP = 3 CP

⇒ \(\frac{{CP}}{{SP}} = \frac{5}{3}\)

⇒ Loss = 5 - 3

⇒ 2

⇒ Loss% = \(\frac{2}{5} × 100 = 40\% \)

∴  Loss % is 40%

Given:

Gain = 19%

Loss = 9%

Concept used:

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

Selling price = (100 – L%)/100 × Cost price

Calculation:

Let the Cost price of the article be 100

Selling price when the gain is 19%

SP = (100 + 19)/100 × 100 = 119

Here, SP is 119% of the CP so the first statement is incorrect

Now, Selling price when the loss is 9%

SP = (100 – 9)/100 × 100 = 91

Here, SP is 91% of the CP so the second statement is also incorrect

∴ The correct answer is option 2

GIVEN:

SP for A / CP for B = 8925

Loss % of A = 15%

Profit % of B = 19% of A's Cp

Spent on repairs = rs 1000

EXPLANATION:

A sold at 15% loss i.e 85% of CP

If 85% of CP is 8925 100% will be = \(\frac{8925}{85}\times100 = 10500\)

CP for A = 10500 

B sells at 19% profit on A's CP i.e = \(\frac{119}{100}\times10500 = 12495\) 

SP for B = 12495

B'sprofit = SP - CP = 12495 - 8925 = 3570

But he spent rs 1000 on repairs

So, actual profit = 3570 - 1000 = 2570

Given:

A shopkeeper has 76 articles of same price. He sells 20 articles at a profit of 15%, 40 at a profit of 19% and the remaining at a profit of 25%. He ends up making a profit of Rs. 27,740. 

Concept used:

Profit and Loss

Calculation:

Let the cost price of each article be Rs.100

A shopkeeper has 76 articles so,

Cost price = 76 × 100 = Rs.7600

20 articles are sold at profit of 15%

⇒ \(20 × \frac{{115}}{{100}} = Rs.23\)

40 articles are sold at 19% 

⇒ \(40 × \frac{{119}}{{100}} = Rs.47.6\)

Remaining 16 articles are sold at 25% profit

⇒ \(16 × \frac{{125}}{{100}} = Rs.20\)

Total selling price = 23 + 20 + 47.6 

Total selling price = 90.60 × 100 = Rs.9060

Profit = 9060 - 7600 = 1460

As per the question,

⇒ 1460 unit = 27740

⇒ 100 unit = \(\frac{{27740}}{{1460}} \times 100\)

∴ CP of one article = Rs1900

GIVEN:

A person sold a table at 6.5% profit. If he had sold it for Rs. 1250 more he would have gained 19%.

FORMULA USED:

SP = CP × [1 + Profit/100]

CALCULATION:

Suppose Cost price = Rs. x

Given,

Difference between 2 selling prices = Rs. 1250

⇒ 119x/100 – 213x/200 = 1250

⇒ 238x/200 – 213x/200 = 1250

⇒ 25x/200 = 1250

⇒ x = 10000

∴ Cost price = Rs. 10000

Given:

Marked price = Rs. 4000

Discount = 10%

Profit = 20%

Formula used:

SP = MP × [(100 – Discount%)/100]

CP = SP × [100/(100 + Gain%)]

Calculation:

SP = Rs. 4000 × (90/100)

⇒ Rs. 3600

CP = Rs. 3600 × (100/120)

⇒ Rs. 3000

∴ The cost price of article is Rs. 3000

Given:

Discount on the list price = 15%

Profit on cost price = 19%

Concept used:

S.P. = C.P. × (100 + Profit %)/100

Indirect process:-

M.P. = S.P. × 100/(100 – discount %)

Calculation:

Let the cost price of the items be 100

Selling price of the items to get 19% profit  = 100 × (100 + 19)/100 = 119

Marked price of the items = 119 × 100/(100 – 15)

⇒ 119 × 100/85

⇒ 11900/85

⇒ 140

Percentage markup on the cost price = (140 – 100)/100 × 100 = 40%
 

∴ The price he should mark on his items to the cost price to get 19% profit would be 40%.