Directions: In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis.
Important for :
1
Quantity I: A shopkeeper bought five toffees in one rupees and marks them up by 25%. If he allows a 12% discount, then how many toffees should be he sell at Rs.22?

Quantity II: A shopkeeper bought four toffees in one rupees and marks them up by 26%. If he allows a 10% discount, then how many toffees should be he sell at Rs.28.35?
» Explain it
D
Quantity I:

 Cost of each toffee = 1 5

As toffees are marked up by 25% then

 Marked price per toffee = 125% of 1 5

Given that discount is 12%

 So, the required selling price per toffee = 88% of 125% of 1 5

 = 88 × 125 × 1 = 0.22 100 × 100 × 5

As, in Rs. 0.22 anyone can buy 1 toffee

 So, in Rs. 1 anyone can buy 1 toffees 0.22

 Thus, in Rs. 22 anyone can buy 1 × 22 = 100 toffees 0.22

Quantity II:
 Cost of each toffee be 1 4

As toffees are marked up by 26% then

 Marked price per toffee = 126% of 1 4

Given that discount is 10%

 So, the required selling price per toffee = 90% of 126% of 1 4

 = 90 × 126 × 1 = 0.2835 100 × 100 × 4

As, in Rs. 0.2835 anyone can buy 1 toffee

 So, in Rs. 1 anyone can buy 1 toffees 0.2835

 Thus, in Rs. 22 anyone can buy 1 × 28.35 = 100 toffees 0.2835

Hence, option (D) is correct.

2
Quantity I:  Rajendra, Ajnish and Narendra are three friends. They have some amount. Rajendra  gave one-third of the amount he had to Ajnish. Ajnish in turn gave half of what he received from Rajendra to Narendra. If the difference between the remaining amount with Rajendra and the amount received by Narendra is Rs. 2500, how much money did Ajnish receive from Rajendra?

Quantity II: Rajendra, Ajnish and Narendra are three friends. They have some amount. Rajendra  gave one-half of the amount he had to Ajnish. Ajnish in turn gave one- fourth of what he received from Rajendra to Narendra. If the difference between the remaining amount with Rajendra and the amount received by Narendra is Rs. 1875, how much money did Ajnish receive from Rajendra?
» Explain it
B
Quantity I :

Suppose initially Rajendra had Rs. y

 Then, amount received by Ajnish = Rs. y 3

 Amount remaining with Rajendra = Rs. ( y – y ) = Rs. 2y 3 3

 Amount received by Narendra = Rs. ( 1 × y ) = Rs. y 2 3 6

 Since, ( 2y – y ) = 2500 3 6

⇒ (4y – y) = 2500 × 6

⇒ 3y = 2500 × 6

⇒ y = 5000.

 Hence, amount received by Ajnish = Rs. y = Rs. 1667 3

Quantity II:

Suppose initially Rajendra had Rs. y
 Then, amount received by Ajnish = Rs. y 2

 Amount remaining with Rajendra = Rs. ( y – y ) = Rs. y 2 2

 Amount received by Narendra = Rs. ( 1 × y ) = Rs. y 4 2 8

 Since, ( y – y ) = 1875 2 8

⇒ (4y – y) = 1875 × 8

⇒ 3y = 1875 × 8

⇒ y = 5000.

 Hence, amount received by Ajnish = Rs. y = Rs. 2500 2

Therefore, option (B) is correct.

3
Quantity I: Elizabeth Farm has only Ostriches and Giant marsupial (4 legs mammal), total count of legs was 14 less than 4 times the total count of heads. How many legs are counted in total?

Quantity II: Elizabeth Farm has only Ostriches and Giant marsupial (4 legs mammal), total count of legs was 15 less than 5 times the total count of heads. How many legs are counted in total?
» Explain it
D

Quantity I:

We know that, Ostriches has 1 head and 2 legs.

Giant marsupial has 1 head and 4 legs

Let number of Ostriches and Giant marsupial be x and y respectively.

According to question,

(2x + 4y) + 14 = 4 × (x + y)

Or, 2x + 4y – 4x – 4y = – 14

Or, –2x = –14

Or, x = 7

So, number of Ostriches = 7

Number of legs = (2x + 4y) = (2 × 7 + 4y) = 14 + 4y

Quantity II:

We know that, Ostriches has 1 head and 2 legs.

Giant marsupial has 1 head and 4 legs

Let number of Ostriches and Giant marsupial be x and y respectively.

According to question,

(2x + 4y) + 15 = 5 × (x + y)

Or, 2x + 4y – 5x – 5y = –15

Or, –3x – y = –15

Or, 3x + y = 15

There is 2 unknown and 1 equation so, exactly we can say anything about x and y. Thus, we cannot calculate number of legs exactly.

Hence, we cannot find any relation between quantity I and quantity II.

Therefore, option (D) is correct.

4
Quantity I: Worker A works 15% faster than Worker B who in turn is 12% faster than Worker C. All three of them work together and earn Rs. 10000. Find the difference between the share of Worker C and Worker A?

Quantity II: Worker A works 20% faster than Worker B who in turn is 10% faster than Worker C. All three of them work together and earn Rs. 9500. Find the difference between the share of Worker C and Worker A?
» Explain it
B
Quantity I:

Let x, y and z be the rates of doing work of Worker A, Worker B and Worker C respectively.

According to question,

x = 1.15y and y = 1.12z

So, x = 1.15y = (1.15 × 1.12)z = 1.288z

Therefore, (x : y : z) = (1.288 : 1.12 : 1)

i.e, the rates of doing work are in the ratio (1.288 : 1.12 : 1)

Hence, earning will be distributed in the ratio (1.288 : 1.12 : 1)

Total earnings, as per the data = Rs. 10000

 Hence the share of Worker A = Rs. 1.288 × 10000 = Rs. 3779 3.408

 And share of Worker C = Rs. 1 × 10000 = Rs. 2934 3.408

Hence the difference between share of the share of Worker C and Worker A = Rs. (3779 – 2934) = Rs. 845

Quantity II:

Let x, y and z be the rates of doing work of Worker A, Worker B and Worker C respectively.

According to question,

x = 1.20y and y = 1.10z

So, x = 1.20y = (1.20 × 1.10) z = 1.32z

Therefore, (x : y : z) = (1.32 : 1.10 : 1)

i.e, the rates of doing work are in the ratio (1.32 : 1.10 : 1)

Hence, earning will be distributed in the ratio (1.32 : 1.10 : 1)

Total earnings, as per the data = Rs. 9500

 Hence the share of Worker A = Rs. 1.32 × 9500 = Rs. 3667 3.42

 And share of Worker C = Rs. 1 × 9500 = Rs. 2778 3.42

Hence the difference between share of the share of Worker C and Worker A = Rs. (3667 – 2778) = Rs. 889

Therefore, option (B) is correct.

5
Quantity I: Rs.12700 was lent in two parts by Swati. One part was lent at 4.5% simple interest per annum (p.a.) and the rest was lent at 11% simple interest p.a. The total interest received from both the parts is Rs.1150 per year. What was the amount lent at 11%p.a?

Quantity II: Rs.12000 was lent in two parts by Swati. One part was lent at 5% simple interest per annum (p.a.) and the rest was lent at 10% simple interest p.a. The total interest received from both the parts is Rs.1200 per year. What was the amount lent at 10%p.a?
» Explain it
B
Quantity I:

Let the amount lent at 11.225% per annum be x

The amount lent at 4.055% per annum be (12700 – x)

According to the question,

 (12700 – x) × 4.055 + x × 11.225 = 1150 100 100

⇒ (12700 × 4.055) – 4.055 × x + 11.225 × x = 1150 × 100

⇒ 51498.5 + 7.17 × x = 115000

⇒ 7.17 × x = 63501.5

⇒ x = 8856.6

Hence, the amount lent at 11.225% per annum be Rs. 8856.6

Quantity II:
Let the amount lent at 10.325% per annum be x

The amount lent at 4.252% per annum be (12000 – x)

According to the question,
 (12000 – x) × 4.252 + x × 10.325 = 1200 100 100

⇒ (12000 × 4.252) – 4.252 × x + 10.325 × x = 1200 × 100

⇒ 51024 + 6.073 × x = 120000

⇒ 6.073 × x = 68976

⇒ x = 11357.8

Hence, the amount lent at 10.325% per annum be Rs. 11357.8

Therefore, option (B) is correct.