**DIRECTIONS for questions (1 to 3): Refer to the data given below and answer the questions that follow.**

The following tables shows the net interest earnings and interest expenses of some banks for years 2003-2004 and 2004-2005:

**All banks do their transactions through loans and fixed deposits only.**

#### Question 1:

**If bank returns for a year are defined as the ratio of interest earnings to interest expenses during that year , then by how much percentage has the bank returns for punj bank increased during 2004-2005 over the previous year?**

b) 10.4%

c) 14.3%

d) 6.8%

e) 4.7%

#### Question 2:

**If issuing loans has got expensive by 10% during the year 2004 – 2005 due to a hike in the annual rates of interest charged by all banks, then for how many of these banks , is there a decrease in loans offered as compared to the previous year ?**

a) 0

b) 1

c) 2

d) 3

e) 4

#### Question 3:

**Which of the following statements is true?**

a) Total loans offered by the five banks during the year 2004- 2005 amount to more than Rs. 200 billions.

b) Exactly three banks have an increase in interest earnings during the year 2004-2005 over the previous year between 5% and 10%

c) Total deposits in the five banks during the year 2004-2005 amount to less than Rs. 160 billions.

d) None of these

a) 238
a) 475
a) 25

b) 30

c) 10

d) 40

e) 20

e) All of these

bank returns during 2003-2004 = 6647/4353 =1.53

Therefore ,

P>S , P >Q , U >S

P/S < P/Q and P/S < U/S

Gives S > Q and U> P

Using (v) , (vi) and (vii) we get the following arrangement ,

T<Q<V<S<P<U<R

So T , Q , V , and S are AP, while S , P , U and R in GP

R/U = U/P = P/S = P/Q - P/S = U/S – P/Q ……… ( i )

P/Q = 2P /S and U/S = 3P/S

U = 3P

U/P = 3

R=1080 , U= 360 , P= 120 AND S= 40

120/Q – 3 = 3

Q=20

b) Exactly three banks have an increase in interest earnings during the year 2004-2005 over the previous year between 5% and 10%

c) Total deposits in the five banks during the year 2004-2005 amount to less than Rs. 160 billions.

d) None of these

**Directions for question 4 to 6: Refer to the data below and answer the questions that follow.**

The sports club in the university organized three major games viz: football, volleyball and basketball. The ratio of the number of students playing football and basketball only and those playing volleyball and basketball only is 2:3. The students playing all the three games are twice the number of students playing football and volleyball only. The numbers of students playing only basketball are 20 less than seven times the number of playing both football and basketball only. The difference in the number of students playing only football and those playing only volleyball is one more than the number of students playing football and volleyball only. The number of students playing all the three games is three more than the number of students playing volleyball and basketball only. Total number of students playing exactly two games is 112.

#### Question 4:

**Find the number of students playing only basketball.**

b) 218

c) 198

d) 358

e) None of these

a) 197

#### Question 5:

**If the number of students playing only football and only volleyball is 366 , then what is the number of students playing only volleyball?**

b) 183

c) 169

d) None of these

e) cannot be determined

a) 10

#### Question 6:

**What is the difference between the students playing all the three games and those playing only football and basketball?**

b) 30

c) 40

d) 50

e) 20

a) 108

**Directions for question (7 - 9): Refer to the data below and answer the questions that follow.**Seven positive numbers P,Q, R ,S,T,U and V arranged in ascending order. Also

(i)The first four numbers are in arithmetic progression.

(ii)The last four numbers are in geometric progression

(iii)P/S , P/ Q , U/S are in increasing arithmetic progression and each of them is greater than 1

(iv) Common difference of the above A.P. ( in iii ) is the same as the common ratio of numbers in geometric progression.

(v) There are two numbers between Q and P

(vi) T is the smallest and R is the greatest the value of R is 1080.

(vii) S is equidistant from Q and U in the arrangement.

#### Question 7:

**Find the value of R/S**

b) 8

c) 216

d) 27

a) 2nd , 65

#### Question 8

**Find the position and value of V in the arrangement ?**

b) 2nd , 20

c) 3rd , 30

d) 3rd , 100

#### Question 9

**Find the value of P-V**

b) 90

c) 25

d) 170

#### Question 10

**In a class, the average marks of n students were 35. When the marks were checked, it was found that marks of a student are taken 10 less than the actual. This leads the average to increase to 36. What is the number of students in the class?**

b) 30

c) 10

d) 40

e) 20

e) All of these

## Answers With Explanation

#### Solution 1

Punjab bank , bank returns during 2004-2005 = 7485/4361 = 1.72bank returns during 2003-2004 = 6647/4353 =1.53

Therefore ,

The percentage increase = ((1.72 – 1.53) / 1.53 )* 100 = (0.19/1.53) * 100

**(a) The percentage increase = 12.6 % approx**#### Solution 2

We do not need to actually calculate the loans offered by all banks.

10% hike in rate of Interest must have increased interest earnings by 10% than the earnings with interest rate before hike

It is sufficient to compare the earnings without hike which are equal to 100 / 110 *earnings during 2004- 2005

10% hike in rate of Interest must have increased interest earnings by 10% than the earnings with interest rate before hike

It is sufficient to compare the earnings without hike which are equal to 100 / 110 *earnings during 2004- 2005

**(D) Three banks have shown a decrease in loans offered.**

#### Solution 3

a) total interest earnings by 5 banks during the year 2004 – 2005 = Rs. 21744 mn

Minimum interest rate charged by any bank = 11%

Maximum loan offered by banks = 21744 * 100/11 < Rs.200000 mn

b) Only Andhra bank has increased in interest earnings between 5% and 10% In the year 2004-2005

c)Total interest expenses during 2004 – 2005 = Rs. 13603

Maximum interest rate on deposits = 8.5 %

Minimum deposits in 5 banks = 13603 * 100 /8.5

8001*20 > Rs.1600000 mn

The number of students playing basketball only is 14y – 20

Let the number of students playing football and volleyball only be x. so , the number of students playing all the three games is 2x

Now ,

2x = 3y +3

(2x/3 – 1 ) = y

X+2y +3y = 112

X+10x / 3 - 5 = 112

The number of students playing only basketball = 14y – 20 = 218 hence

Let the number of students playing football be ‘a’ and those playing volleyball be ‘b’

a-b = x+1 = 28 ….. (1)

a+b = 366 ……………(2)

solving equation (1) and (2) weget ,

a=197 and b=169

The number of students playing all the three games is 2x = 54 and those playing only football and basketball is 2y= 34

Minimum interest rate charged by any bank = 11%

Maximum loan offered by banks = 21744 * 100/11 < Rs.200000 mn

**Hence statement I is false.**b) Only Andhra bank has increased in interest earnings between 5% and 10% In the year 2004-2005

**Statement (b) is false**c)Total interest expenses during 2004 – 2005 = Rs. 13603

Maximum interest rate on deposits = 8.5 %

Minimum deposits in 5 banks = 13603 * 100 /8.5

8001*20 > Rs.1600000 mn

**Statement ( c ) is false****Hence (d) none of these**#### Solution 4-6

Let the number of students playing football and basketball only be 2y. so the number of students playing volleyball and basketball only is 3yThe number of students playing basketball only is 14y – 20

Let the number of students playing football and volleyball only be x. so , the number of students playing all the three games is 2x

Now ,

2x = 3y +3

(2x/3 – 1 ) = y

X+2y +3y = 112

X+10x / 3 - 5 = 112

**Thus we get x =27 and y = 17**The number of students playing only basketball = 14y – 20 = 218 hence

**(b) is the right answer for Question 4**Let the number of students playing football be ‘a’ and those playing volleyball be ‘b’

a-b = x+1 = 28 ….. (1)

a+b = 366 ……………(2)

solving equation (1) and (2) weget ,

a=197 and b=169

**Hence ( c ) is the right answer for Question 5**The number of students playing all the three games is 2x = 54 and those playing only football and basketball is 2y= 34

**Hence (E) is the right answer for Question 6.**

#### Solution 7 - 9

**From (iii) and (iv)**

P>S , P >Q , U >S

P/S < P/Q and P/S < U/S

Gives S > Q and U> P

Using (v) , (vi) and (vii) we get the following arrangement ,

T<Q<V<S<P<U<R

So T , Q , V , and S are AP, while S , P , U and R in GP

**From (ii) and (iii),**

R/U = U/P = P/S = P/Q - P/S = U/S – P/Q ……… ( i )

P/Q = 2P /S and U/S = 3P/S

U = 3P

U/P = 3

**So the common ratio of the geometric progression is 3**

R=1080 , U= 360 , P= 120 AND S= 40

**Substituting values of P and S in equation (i)**

120/Q – 3 = 3

Q=20

Since

S-Q = 20 = 2d , where d is the common difference of the four numbers is arithmetic progression

T= 10 , G= 20 and V = 30

The required arrangement is 10 , 20 , 30 , 40 , 120 , 360 , 1080

T= 10 , G= 20 and V = 30

The required arrangement is 10 , 20 , 30 , 40 , 120 , 360 , 1080

#### Solution 10

Let T be the total marks of the ‘n’ students originally, then T/n = 35 but actually T+10 / n = 36

Which gives n = 10

Which gives n = 10

**Hence ( c) is the correct answer.**

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