Comparing Quantities Test

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Comparing Quantities Test - 55

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Question 1
1 / -0

A loss of $$20$$% is incurred when $$6$$ articles are sold for a rupee. To gain $$20$$% how many articles should be sold for a rupee?

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Given than, $$SP = 1, Loss$$% $$= 20$$%
We know that, $$SP = 0.8\times CP$$
$$CP = \dfrac {5}{4}$$
To gain $$20$$%, $$SP = 1.2\times CP = \dfrac {120}{100}\times \dfrac {5}{4} = \dfrac {3}{2} \Rightarrow SP = \dfrac {3}{2}$$
For $$Rs. 3/2$$ number of articles sold $$= 6$$
For $$Rs. 1$$ number of articles to be sold $$= 6\times \dfrac {2}{3} = 4$$ articles.
Question 2
1 / -0

A, B, C enter into partnership. A invests some money at the beginning, B invests double the amount after $$6$$ months and C invests thrice the amount after $$8$$ months. If the annual profit is Rs$$27,000$$. C's share is (in Rs)

A
$$11,250$$

B
$$9,000$$

C
$$10,800$$

D
$$8,625$$

Solution

Let the amount A invest is Rs$$x$$.
Time period of investment of A is $$12$$ months.
Amount B invest is Rs$$2$$x.
Time period of investment of B is $$6$$ months.
Amount C investment is Rs$$3$$x.
Time period of investment of C is $$4$$ months.
Profit is divided in the ratio = Amount of investment \times Time period of investment
$$P_A : P_B : P_C = x \times 12 : 2x \times 6 : 3x \times 4$$
=$$12 x : 12 x : 12 x$$
=$$1 : 1 : 1$$
C's share of profit = $$\dfrac{1}{3} \times 27000 = 9000$$
Question 3
1 / -0

A house and store were sold for $$\text{Rs. } 12,000$$ each. The house was sold at a loss of $$20\%$$ of the cost and the store at a gain of $$20\%$$ of the cost. The entire transaction resulted in

A
No loss or gain

B
Loss of $$\text{Rs. } 1000$$

C
Gain of $$\text{Rs. } 1000$$

D
Gain of $$\text{Rs. } 2000$$

E
None of these

Solution

$$12,000 = H - \dfrac {1}{5}H \therefore H = 15,000$$
$$12,000 = S + \dfrac {1}{5}S \therefore S = 10,000$$
$$ H + S = 25,000$$.
Therefore, the sale resulted in a loss of $$Rs. 1000$$.
Question 4
1 / -0

Select the ratio that is equivalent to $$12:14$$

A
$$6:2$$

B
$$6:7$$

C
$$3:8$$

D
$$5:7$$

Solution

Given ratio is $$12:14$$
It can be rewritten as $$\dfrac{12}{14}=\dfrac{6\times 2}{7\times 2}$$
Cancelling $$2$$ from numerator and denominator, we get
$$\dfrac{12}{14}=\dfrac{6}{7}$$ i.e $$6:7$$
Hence, the answer is $$6:7$$.
Question 5
1 / -0

A shop keeper earns a profit of $$12$$% on selling a book at $$10$$% discount on the printed price. The ratio of cost price to the printed price of the book is

A
$$45 : 56$$

B
$$50 : 61$$

C
$$99 : 125$$

D
None of these

Solution

Using the formula
$$\dfrac {100\pm (Profit\ Loss)}{100 - Discount} = \dfrac {M.P}{C.P}$$
$$\dfrac {M.P}{C.P} = \dfrac {112}{100 - 10} = \dfrac {112}{90} = \dfrac {56}{45}$$
Hence, $$\dfrac {C.P}{M.P} = \dfrac {45}{56}$$.
Question 6
1 / -0

Mr,A owns a home worth Rs.$$10,000$$. He sells it to Mr.B at a $$10\%$$ profit based on the worth of the house. Mr.B sells the house back to Mr.A at a $$10\%$$ loss. Then:

A
A comes out even

B
A makes Rs.$$1100$$ on the deal

C
A makes Rs.$$1000$$ on the deal

D
A loses Rs.$$900$$ on the deal

Solution

$$\text{C.P. of B = 110% of Rs. 10000 = Rs. 11000}$$
$$\text{Loss of B = 10%}$$
$$\text{S.P. of B = 90% of Rs. 11000 = Rs. 9900}$$
$$\text{Thus, C.P. of A = Rs. 9900}$$
$$\text{So, A gets [(10% of Rs. 10000) + (10000 - 9900)] = Rs. 1100}$$
Question 7
1 / -0

The cost $$C$$ of sending a parcel post package weighing $$P$$ gms, $$P$$ an integer is $$Rs. 10$$ for the first grams and $$Rs. 3$$ for each additional grams. The formula for the cost is

A
$$C = 10 + 3P$$

B
$$C = 10P + 3$$

C
$$C = 10 + 3 (P - 1)$$

D
$$C = 9 + 3P$$

E
$$C = 10P - 7$$

Solution

For $$P - 1$$ gms the charge is $$3$$ rupees per grams. For the first gram the charge is $$10$$ rupees. $$\therefore C = 10 + 3(P - 1)$$; or
The charge for each gram is $$3$$ rupees with an additional charge of $$7$$ rupees for the first gram. $$\therefore C = 3P + 7 = 3P - 3 + 10 = 10 + 3(P - 1)$$.
Question 8
1 / -0

$$5$$% more is gained by selling a watch for $$Rs. 350$$ than by selling it for $$Rs. 340$$. The cost price of the watch is

A
$$Rs. 110$$

B
$$Rs. 140$$

C
$$Rs. 200$$

D
$$Rs. 250$$

Solution

Let cost price be $$Rs. x$$
Then $$5$$% of $$x = (350 - 340)$$
$$5$$% of $$x = 10$$
$$x = 10\times \dfrac {100}{5} = 200$$
Hence, cost price is $$Rs. 200$$.
Question 9
1 / -0

Tanishka deposited Rs. $$50,000$$ in a bank for two years with the interest rate of $$5.5\%$$ p.a. How much interest would she earn?

A
$$6,000$$

B
$$5,250$$

C
$$55,500$$

D
$$5,500$$

Solution

$$ Interest = \cfrac{ 50000 \times 2 \times 5.5 }{100} = 5500$$
Question 10
1 / -0

A sum of money invested at 14$$\%$$ per annum amounted to Rs. 10400 in 5 years. Calculate the principal.

A
$$Rs.\ 6067.34$$

B
$$Rs.\ 6278.24$$

C
$$Rs.\ 6384.62$$

D
$$Rs.\ 6117.65$$

Solution

We have the formula for amount in simple interest as:

$$A=P(1+rt)$$

Given, $$A=10400$$, $$t=5$$, $$r=14\%$$

$$\therefore \ 10400=P(1+5(0.14))$$

$$10400=P(1+0.7)=P(1.7)$$

$$P=\dfrac{10400}{1.7}$$

$$=6117.647.6$$

Hence, the principal amount is Rs. $$6117.65$$.

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 55

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Comparing Quantities Test - 55

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SHARING IS CARING

Question 1

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 2

$$11,250$$

$$9,000$$

$$10,800$$

$$8,625$$

Solution

Question 3

No loss or gain

Loss of $$\text{Rs. } 1000$$

Gain of $$\text{Rs. } 1000$$

Gain of $$\text{Rs. } 2000$$

None of these

Solution

Question 4

$$6:2$$

$$6:7$$

$$3:8$$

$$5:7$$

Solution

Question 5

$$45 : 56$$

$$50 : 61$$

$$99 : 125$$

None of these

Solution

Question 6

A comes out even

A makes Rs.$$1100$$ on the deal

A makes Rs.$$1000$$ on the deal

A loses Rs.$$900$$ on the deal

Solution

Question 7

$$C = 10 + 3P$$

$$C = 10P + 3$$

$$C = 10 + 3 (P - 1)$$

$$C = 9 + 3P$$

$$C = 10P - 7$$

Solution

Question 8

$$Rs. 110$$

$$Rs. 140$$

$$Rs. 200$$

$$Rs. 250$$

Solution

Question 9

$$6,000$$

$$5,250$$

$$55,500$$

$$5,500$$

Solution

Question 10

$$Rs.\ 6067.34$$

$$Rs.\ 6278.24$$

$$Rs.\ 6384.62$$

$$Rs.\ 6117.65$$

Solution

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