**1. ANSWER : C**

** Explanation - ** Number of students who passed half-yearly exams in the school

= (Number of students passed in half-yearly but failed in annual exams) + (Number of students passed in both exams)

= (6 + 17 + 9 + 15) + (64 + 55 + 46 + 76)

= 288.

Also, Number of students who passed annual exams in the school

= (Number of students failed in half-yearly but passed in annual exams) + (Number of students passed in both exams)

= (14 + 12 + 8 + 13) + (64 + 55 + 46 + 76)

= 288.

Since, the number of students passed in half-yearly = the number of students passed in annual exams. Therefore, it can be inferred that both the examinations had almost the same difficulty level.

Thus Statements (a), (b) and (d) are false and Statement (c) is true.

**2. ANSWER : D**

**Explanation - **Since the classification of the students on the basis of their results and sections form independent groups, so the total number of students in the class:

= (28 + 23 + 17 + 27 + 14 + 12 + 8 + 13 + 6 + 17 + 9 + 15 + 64 + 55 + 46 + 76)

= 430.

**3. ANSWER : D**

**Explanation****- **Pass percentages in at least one of the two examinations for different sections are:

For Section A = $\frac{14+6+64}{28+14+6+64}\times 100=\frac{84}{112}\times 100$% = 75%

For Section B =$\frac{12+17+55}{23+12+17+55}\times 100$ % = 78.5%

For Section C = $\frac{8+9+46}{17+8+9+46}\times 100$%= 78.75%

For Section D = $\frac{13+15+76}{27+13+15+76}\times 100$%= 79.39%

Clearly ,the pass percentage is maximum for Section D

**4. ANSWER : A**

**Explanation - **Total number of students passed in annual exams in a section

= [ (No. of students failed in half-yearly but passed in annual exams) + (No. of students passed in both exams) ] in that section

Success rate in annual exams in Section A= $\frac{14+64}{112}\times 100$% = 69.64%

Similarly, success rate in annual exams in:

Section B = $\frac{12+55}{107}\times 100$% = 62.62%

Section C = $\frac{8+46}{80}\times 100$% = 67.5%

Section D = $\frac{89}{131}\times 100$% = 67.94%

Clearly, the success rate in annual examination is maximum for Section A.

**5. ANSWER : D**

**Explanation - **Total number of failures in half-yearly exams in a section

= [ (Number of students failed in both exams) + (Number of students failed in half-yearly but passed in Annual exams) ] in that section

Failure rate in half-yearly exams in Section A %= 37.5 %

Similarly, failure rate in half-yearly exams in:

Section B = 32.71%

Section C = 31.25%

Section D = 30.53%

Clearly, the failure rate is minimum for Section D.

= (Number of students passed in half-yearly but failed in annual exams) + (Number of students passed in both exams)

= (6 + 17 + 9 + 15) + (64 + 55 + 46 + 76)

= 288.

Also, Number of students who passed annual exams in the school

= (Number of students failed in half-yearly but passed in annual exams) + (Number of students passed in both exams)

= (14 + 12 + 8 + 13) + (64 + 55 + 46 + 76)

= 288.

Since, the number of students passed in half-yearly = the number of students passed in annual exams. Therefore, it can be inferred that both the examinations had almost the same difficulty level.

Thus Statements (a), (b) and (d) are false and Statement (c) is true.

Exam Prep: CAT , Bank Exams , AIEEE

Job Role: Bank PO , Bank Clerk , Analyst

A) 9 lakhs | B) 6 lakhs |

C) 3 lakhs | D) 2 lakhs |

Explanation:

Educated females in city P = 25 lakhs

Uneducated females in city P = 30 - 25 = 5 lakhs

Educated males city S = 21 lakhs

Educated males in city S = 35 - 21= 14 lakhs

Required difference = 14 - 5 = 9 lakhs

**1. Answer : 4**

**Explanation : **Let the borrowing of Company A = x

Interest of Company A = 234000

Rate of Interest = 18%

$\therefore x\times \frac{18}{100}=234000\Rightarrow x=1300000$

Let the borrowing of Company B = y

Interest of Company B = 576000

Rate of interest = 24%

$\therefore y\times \frac{24}{100}=576000\Rightarrow y=2400000$

Required difference = y - x = 2400000 - 1300000 = Rs. 1100000

**2. Answer : 2**

**Explanation : **

Let the profit of Comapny B = 100%

Dividend Payout ratio(%) of B = 19.60

Remaining percent i.e retained earning = 100 - 19.60 = 80.4%

According to question, 80.4% = Rs.402 lakh

100% = Rs.500 lakh

Therefore, Total dividend paid by Company B = 500 - 402 = Rs. 98 lakh

Let the profit of company D = 100%

Dividend payout ratio (%) of D = 32.50

Remaining percent i.e retained earning = 100 - 32.50 = 67.5%

According to question, 67.5% = Rs. 270 lakh

100% = Rs. 400 lakh

Therefore, Total dividend paid by company D = 400 - 270 = Rs. 130 lakh

Required difference = 130 - 98 = Rs. 32 lakh

**3. Answer : 3**

**Explanation : **

Let the profit of Company C = 100%

Dividend payout ratio of C = 8.75%

Remaining percent i.e, retained earning = 100 - 8.75 = 91.25

According to question, 91.25% = Rs. 365 lakh

100% = Rs. 400 lakh

Therefore, Profit of C = Rs. 400 lakh

Let the profit of company E = 100%

Dividend payout ratio of E = 28%

Remaining percent i.e retained earning = 100 - 28 = 72%

According to question, 72% = Rs.216 lakh

100% = Rs.300 lakh

Therefore, Profit of E = Rs. 300 lakh

Required percentage = $\frac{100}{400}\times 100$ = 25% less

**4. Answer : 3**

**Explanation : **

Profit made by company A = Rs. 200 lakh

Profit made by company B = Rs. 500 lakh

Required Sum = 200 + 500 = Rs. 700 lakh

**5. Answer : 4**

**Explanation : **

Required Sum = 1300000 + 2400000 + 810000 + 1600000 + 1200000 = 7310000 = Rs. 73.1 lakh

**1. ANSWER : D**

**Explanation - **Required difference

= (272 + 240 + 236 + 256 + 288) - (200 + 224 + 248 + 272 + 260)

= 88.

**2. ANSWER : B**

**Explanation - **Total number of Peons working in the Company in 1999

= (820 + 184 + 152 + 196 + 224) - (96 + 88 + 80 + 120)

= 1192.

**3. ANSWER : A**

**Explanation -** Number of Managers working in the Company:

In 1995 = 760.

In 2000 = (760 + 280 + 179 + 148 + 160 + 193) - (120 + 92 + 88 + 72 + 96)= 1252.

Therefore, Percentage increase in the number of Managers

=$\frac{\left(1252-760\right)}{760}\times 100$ %= 64.74%

Number of Technicians working in the Company:

In 1995 = 1200.

In 2000 = (1200 + 272 + 240 + 236 + 256 + 288) - (120 + 128 + 96 + 100 +112) = 1936.

Therefore, Percentage increase in the number of Technicians

= $\frac{\left(1936-1200\right)}{1200}\times 100$ % = 61.33%

Number of Operators working in the Company:

In 1995 = 880.

In 2000 = (880 + 256 + 240 + 208 + 192 + 248) - (104 + 120 + 100 + 112 + 144) = 1444.

Therefore, Percentage increase in the number of Operators

=$\frac{\left(1444-880\right)}{880}\times 100$ % = 64.09%

Number of Accountants working in the Company:

In 1995 = 1160.

In 2000 = (1160 + 200 + 224 + 248 + 272 + 260) - (100 + 104 + 96 + 88 + 92) = 1884.

Therefore, Percentage increase in the number of Accountants

=$\frac{\left(1884-1160\right)}{1160}\times 100$ % = 62.14%

Number of Peons working in the Company:

In 1995 = 820.

In 2000 = (820 + 184 + 152 + 196 + 224 + 200) - (96 + 88 + 80 + 120 + 104) = 1288.

Therefore, Percentage increase in the number of Peons

=$\frac{\left(1288-820\right)}{820}\times 100$ % = 57.07%

Clearly, the percentage increase is maximum in case of Managers.

**4. ANSWER : B**

**Explanation - ** Total number of employees of various categories working in the Company in 1997 are:

Managers = (760 + 280 + 179) - (120 + 92) = 1007.

Technicians = (1200 + 272 + 240) - (120 + 128) = 1464.

Operators = (880 + 256 + 240) - (104 + 120) = 1152.

Accountants = (1160 + 200 + 224) - (100 + 104) = 1380.

Peons = (820 + 184 + 152) - (96 + 88) = 972.

Therefore, Pooled average of all the five categories of employees working in the Company in 1997 = 1/5 x (1007 + 1464 + 1152 + 1380 + 972)

= 1/5 x (5975)

= 1195.

**5. ANSWER : D**

**Explanation - ** Total number of Operators who left the Company during 1995 - 2000

= (104 + 120 + 100 + 112 + 144)

= 580.

Total number of Operators who joined the Company during 1995 - 2000

= (880 + 256 + 240 + 208 + 192 + 248

= 2024.

Therefore, Required Percentage

= (580/2024)x100% = 28.66% ~= 29%.

**1. ANSWER : D**

**Explanation - **

Average amount of interest paid by the company during the given period

=$Rs.\frac{23.4+32.5+41.6+36.4+49.4}{5}lakhs=Rs.\frac{183.3}{5}lakhs$

= Rs. 36.66 lakhs** **

**2. ANSWER : C**

**Explanation - **

Required Percentage = $\frac{3.00+2.52+3.84+3.68+3.96}{288+342+324+336+420}\times 100$ %

= $\frac{17}{1710}\times 100$% $\approx $1%

**3. ANSWER: C**

**Explanation - **** **

Required Percentage = $\frac{288+98+3.00+23.4+83}{420+142+3.96+49.4+98}\times 100$

= $\frac{495.4}{713.36}\times 100$ $\approx $ 69.45%

**4. ANSWER: A**

**Explanation - **Total expenditure of the Company during 2000 = (324 + 101 + 3.84 + 41.6 + 74) lakhs = 544.44 lakhs

**5. ANSWER : B**

**Explanation - **

Required ratio = $\frac{83+108+74+88+98}{98+112+101+133+142}$

= $\frac{451}{586}$

= ** $\frac{1}{1.3}=\frac{10}{13}$ **