Comparing Quantities Test

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Comparing Quantities Test - 55

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Weekly Quiz Competition

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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Comparing Quantities Test - 55

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Comparing Quantities Test - 55

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SHARING IS CARING

Question 1

111

222

333

444

Solution

Question 2

11,25011,25011,250

9,0009,0009,000

10,80010,80010,800

8,6258,6258,625

Solution

Question 3

No loss or gain

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

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

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

None of these

Solution

Question 4

6:26:26:2

6:76:76:7

3:83:83:8

5:75:75:7

Solution

Question 5

45:5645 : 5645:56

50:6150 : 6150:61

99:12599 : 12599:125

None of these

Solution

Question 6

A comes out even

A makes Rs.110011001100 on the deal

A makes Rs.100010001000 on the deal

A loses Rs.900900900 on the deal

Solution

Question 7

C=10+3PC = 10 + 3PC=10+3P

C=10P+3C = 10P + 3C=10P+3

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

C=9+3PC = 9 + 3PC=9+3P

C=10P−7C = 10P - 7C=10P−7

Solution

Question 8

Rs.110Rs. 110Rs.110

Rs.140Rs. 140Rs.140

Rs.200Rs. 200Rs.200

Rs.250Rs. 250Rs.250

Solution

Question 9

6,0006,0006,000

5,2505,2505,250

55,50055,50055,500

5,5005,5005,500

Solution

Question 10

Rs. 6067.34Rs.\ 6067.34Rs. 6067.34

Rs. 6278.24Rs.\ 6278.24Rs. 6278.24

Rs. 6384.62Rs.\ 6384.62Rs. 6384.62

Rs. 6117.65Rs.\ 6117.65Rs. 6117.65

Solution

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$1$

$2$

$3$

$4$

$11,250$

$9,000$

$10,800$

$8,625$

Loss of $\text{Rs. } 1000$

Gain of $\text{Rs. } 1000$

Gain of $\text{Rs. } 2000$

$6:2$

$6:7$

$3:8$

$5:7$

$45 : 56$

$50 : 61$

$99 : 125$

A makes Rs. $1100$ on the deal

A makes Rs. $1000$ on the deal

A loses Rs. $900$ on the deal

$C = 10 + 3P$

$C = 10P + 3$

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

$C = 9 + 3P$

$C = 10P - 7$

$Rs. 110$

$Rs. 140$

$Rs. 200$

$Rs. 250$

$6,000$

$5,250$

$55,500$

$5,500$

$Rs.\ 6067.34$

$Rs.\ 6278.24$

$Rs.\ 6384.62$

$Rs.\ 6117.65$