Arithmetic Aptitude MCQ (Multiple Choice Questions)

The correct answer is “14 \frac{2}{7} \% \text { profit }“
Question: 100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is:

Step by Step Solution:

Step: 1
The cost price of 100 oranges = RS. 350
The cost price of 1 orange will be = \frac{350}{100}
The cost price of 1 Orange = RS. 3.50

Step: 2
The sale price of 12 oranges = RS. 48
The sale price of 1 orange will be = \frac{48}{12}
The sale price of 1 orange = RS. 4

Step: 3
As the selling price is more than the cost price, it means there is gain; so will use the gain % formula.

\text { Gain } \%\ =\ \left(\frac{Selling\ price\ -\ Cost\ price}{Cost\ price}\ \times\ 100\right)\%

\text { Gain } \%\ =\ \left(\frac{4\ -\ 3.50}{3.50}\ \times\ 100\right)\%

\text { Gain } \%=\left(\frac{0.50}{3.50} \times 100\right) \%

\text { Gain } \%=\frac{100}{7} \%

by simplifying more;

\text { Gain } \%=14 \frac{2}{7} \% or 14.28%

Hence, the Gain percentage is 14 \frac{2}{7} \% \text { loss }

The correct answer is “25300”.

QUESTION: When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?

Step by Step Solution:

In the problem, we know the selling price and loss %, but we don’t know the cost price.

Let Cost Price is X= 100%
∴ Loss = Cost price – Selling price
then,
Selling price = Cost price – Loss
Selling price = 100% – 15%
S.P = 85%

According to the problem statement

S.P = 85% = RS. 18700
Now,

85% of X = RS. 18700

\frac{85}{100}\ x\ =\ RS. 18700

x\ =\ \frac{RS. 18700}{85}\ \times\ 100

x\ =\ RS. 22000

So now we find C. P = RS. 22000
Hence,
Gain = C. P – S. P
Gain amount = RS. 22000 – RS. 18700
Gain = RS. 3300

Therefore, by final condition.

As we assumed cost price at 100%, so

Cost price = 100% = RS. 22000,
Total gain to find = 100% + 15% =115%

The new selling price to gain 15% is equal to 115% of the cost price (RS. 22000)

S.P to gain 15% = \frac{115}{100}\ \times\ RS. 22000

Selling price to gain 15% = RS. 25300

Hence, The plot must be sold at RS. 25300 to get a 15% gain.

The correct answer is “60”.
On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:

Step by Step Solution:

We know that;

Loss = Cost price – Selling Price

According to the statement, Put values in the above formula

(Cost Price of 5 balls) = (Cost Price of 17 balls) – (Selling Price of 17 balls)

(C.P of 17 balls) – (C.P of 5 balls) = Selling Price of 17 balls

C.P of 12 balls = S.P of 17 balls

According to the above equation, the Selling price of 17 balls is equal to the cost price of 12 balls.

As we know, the selling price of 17 balls is RS. 720, the cost price of 12 balls will also be RS. 720.

C.P of 12 balls = RS. 720

C.P of 1 ball would be = RS. \frac{720}{12}

C.P of 1 ball = RS. 60

Hence the cost price of 1 ball is Rs. 60

The correct answer is “44%”.

Step by step Solution:

According to the problem statement,
⇒ The cost price of 6 articles is 5, then the cost price of 1 article would be RS \cdot \frac{5}{6}

⇒ The selling price of 5 articles is 6, then the selling price of 1 article would be RS \cdot \frac{6}{5}

Now Gain % Formula is,

Gain% =\frac{\text { (selling price – cost price) }}{\text { cost price }} \times 100

By putting Values, it will be

\frac{\left(\frac{6}{5}-\frac{5}{6}\right)}{\left(\frac{5}{6}\right)} \times 100

Taking LCM of Cost price and Selling price,

\frac{\left(\frac{36-25}{30}\right)}{\left(\frac{5}{6}\right)} \times 100

\frac{\left(\frac{11}{30}\right)}{\left(\frac{5}{6}\right)} \times 100

\left(\frac{11}{30}\right) \times\left(\frac{6}{5}\right) \times 100


\begin{array}{l}\frac{11\ \times\ 6}{30\ \times5}\ \times100\ ⇒\frac{66}{150}\ \times\ 100\ ⇒\frac{6600}{150}\ =\ 44\ \%\end{array}

Alternate Solution:

You can calculate gain % by simple method;
let’s suppose we have bought the number of articles, take LCM of 6 and 5, it is 30.
Now, as we know the number of articles bought, we can calculate Cost price and selling price.

Cost price =R s .\left(\frac{5}{6} \times 30\right)=R s .25

Selling Price =R s .\left(\frac{6}{5} \times 30\right)=R s .36

Now, by putting values in the Gain% formula

Gain% =\frac{\text { (selling price – cost price) }}{\text { cost price }} \times 100

Gain% =\frac{\text { (RS. 36 – RS. 25) }}{\text { RS. 25 }} \times 100

Gain% =\frac{\text { (RS. 11) }}{\text { RS. 25 }} \times 100

Gain% = 44%
Thus, Gain% is 44%.

The correct answer is “5.6 %“

Step by step Solution:

We are given,

a) 20 dozen toys, each dozen toys have a cost price of RS. 375
b) 1 toy selling price is RS. 33

Now to find 1 toy cost price, we will divide 1 dozen toys cost price by 12, as we know dozen contains 12 items. so,

\text { C.P. }=\text { Rs. }\left(\frac{375}{12}\right)

The cost price of 1 toy = 31.25

Now we have both cost price and selling price of 1 toy, so we can calculate the profit percentage by given formula.

Profit % = \frac{Selling price-Cost price}{Cost price} \times 100

By putting value, we will have;

Profit % = \frac{RS. 33-RS. 31.25}{RS. 31.25} \times 100

Profit % = \frac{28}{5}\%

Profit % = 5.6%

Hence, Sam has a percentage profit of 5.6

Note:

You can also solve this problem by first calculating the profit amount and then applying the profit% formula, but it will be lengthy, also data of 20 dozen is irrelevant and we don’t need that data to find profit %.

Profit% and Gain % are interchangeable names of each other.

The correct answer is “Rs 1190”

Step by Step Solution:
Given: A man buying a cycle for Rs 1400 and selling it for a loss of 15%.
Find: Selling price?

We know that cost price is the price at which we bought any item, while selling price is the price at which we sold any item.

Now, let’s calculate loss which is 15% of the actual price or buying price of 1400

⇒ \frac{15}{100}\ of\ 1400\ =\ \frac{15}{100}\times1400

Loss Amount ⇒ 0.15 × 1400 = RS. 210

According to the loss formula now we can find the selling price

Loss = cost price – selling price
so selling price would be
⇒ Selling price = cost price – loss

By putting values, we get

Selling price = RS. 1400 – RS. 210

⇒ Selling price = RS. 1190

Hence, the selling price of the cycle is RS. 1190.

Note: You can also use this formula

\text { Selling price = Original Price }\left(1 \pm \frac{r}{100}\right)

Where “r” is the profit/loss percentage, and + sign is used when profit% is given while the -sign is used when loss% is given.

The correct answer is “Rs. 72”.
Step by Step Solution:
According to the problem statement, the expected gain on cost price (CP) is 22.5%, while the expected sale price is RS. 392.

We are given the gain % of 25% and the sale price of RS. 392, while cost price is unknown, so we will first find cost price.
According to the profit % or gain %,

\text { (gain) } \%=\frac{\text { selling price }-\cos t \text { price }}{\cos t \text { price }} \times 100

22.5 =\frac{392-C P}{C P} \times 100

\frac{22.5}{100} C P=392-C P

0.225 CP = 392−CP

Now, taking -CP from right side to left side of the equation, it will become +CP

0.225 CP+CP = 392

1.225 CP =3 92

Divide both sides by 1.225, we have

C P=\frac{392}{1.225}

CP=Rs.320

Now we have calculated the cost price, and we already have the sale price, so we can calculate the profit by this formula,

Profit = Sale price – cost price

Profit = RS. 392 – RS. 320

Profit = Rs. 72

So the shopkeeper’s profit is RS. 72

The correct answer is “Rs. 2000”.
Step by Step Solution:
suppose the cost price of the product is Rs. X
Remember these formulas for Profit % and Loss %

\text { profit) } \%=\frac{\text { selling price }-\cos t \text { price }}{\cos t \text { price }} \times 100

(\text { loss }) \%=\frac{\cos t \text { price }-\text { selling price }}{\cos t \text { price }} \times 100

According to the problem statement, the percentage profit is equal to the percentage loss incurred.

Profit % = Loss %

\frac{\text { selling price }-\cos t \text { price }}{\cos t \text { price }} \times 100 = \frac{\cos t \text { price }-\text { selling price }}{\cos t \text { price }} \times 100

\frac{1920-x}{x} \times 100=\frac{x-1280}{x} \times 100

“X and 100” on both sides of the equation will cancel each other.
then we will have
⇒ 1920−x = x−1280
⇒ 2x = 3200
⇒ x = 1600
Now, for-profit of 25%
we will use this formula

Profit% =\frac{\text { (selling price – cost price) }}{\text { cost price }} \times 100

25 =\frac{\text { (selling price – 1600) }}{\text { 1600 }} \times 100

\frac{25\times1600}{100} = Selling price – 1600

400 = Selling price – 1600
Selling price to gain 25% = 400+1600
Selling price to gain 25% = 2000

So the article should be sold at 2000 to make a 25% profit.

The correct answer is (C)“5”.
Step-by-step Solution:
According to the problem statement,
The cost price (CP) of 6 toffees = Rs. 1
So according to the unitary method,

The cost price of 1 toffee = RS. \frac{1}{6}

Now we will use this formula to gain 20%

=\frac{\text { (selling price – cost price) }}{\text { cost price }} \times 100

1 toffee SP will be
20=\frac{\left(\text { selling price }-\frac{1}{6}\right)}{\frac{1}{6}} \times 100

\frac{20}{100} \times \frac{1}{6}=\text { (selling price of } 1 \text { toffee) }-\frac{1}{6}

=\frac{1}{5} \times \frac{1}{6}=(\text { SP of } 1 \text { toffee })-\frac{1}{6}

=\frac{1}{5} \times \frac{1}{6}+\frac{1}{6}=\text { (SP of } 1 \text { toffee) }

=\frac{1}{6}\left(1+\frac{1}{5}\right)=(\text { SP of } 1 \text { toffee })

=(\text { SP of } 1 \text { toffee })=\frac{1}{6} \times\left(\frac{6}{5}\right)
So,
The selling price (SP) of 1 toffee is RS. \frac{1}{5}

∴ According to the unitary method, 5 toffees selling price will be = 1

The vendor must sell 5 toffees for a rupee to gain 20%.

The correct answer is “70%”.
Step by Step Solution:
Let’s assume
The initial cost price (CP) is 100.
The profit (p) is 320%
we know that ⇒ 320% of 100 = 320
We know that ⇒ Profit (P)= SP-CP
so,
The Selling Price (SP) ⇒ SP = CP +P
By putting values,
SP = 100+320 ⇒ 420
Now if CP increases by 25%
Then, the new cost price (CP1) is 100+25=125.
according to the problem condition, SP remains constant at 420
New profit (P1) = SP – CP1
P1= 320-125 ⇒ 295
Now we have to convert the new profit in percentage