The table given below shows the percentage break-up of the Gross Domestic Expenditure on four areas - Basic

Research (BR), Applied Research (AR), Experimental Development Research (EDR) and Miscellaneous Research (MR) – of Research and Development (R&D) activity by a country in the period 2008-12.

R & D | 2008 | 2009 | 2010 | 2011 | 2012 |
---|---|---|---|---|---|

BR | 10.7 | 15 | 30.5 | 45.5 | 19.5 |

AR | 22.8 | 20.6 | 20.4 | 14.4 | 11.5 |

EDR | 62 | 55.4 | 35.4 | 32.4 | 64.2 |

MR | 4.5 | 9 | 13.7 | 7.7 | 4.8 |

Q1. If the expenditure on AR in 2011 was 20% more than that in 2010, then by what percent was the expenditure on EDR in 2011 more than that in 2010?

a) 55.6

b) 50.4

c) 66.5

d) 45.8

Q2. If the expenditure on R&D was equal in all the years during the given period, then how many areas witnessed a continual increase in expenditure during the given period?

a) 3

b) 1

c) 2

d) 0

Q3. If the absolute difference between the expenditures on BR and AR in 2011 was $46.65 mn and that in 2012 was$16 mn, then the total expenditure on R&D in 2012 was what percent more than that in 2011?

a) 25.00

b) 33.33

c) 66.67

d) 35.00

Solution :

Q1) Suppose Total expenditure was P in 2010 and K in 2011.

P (0.204) x 1.2 = K (0.144)

1.7 P = K.

Expenditure on EDR in 2010 = 0.354 P.

Expenditure on EDR in 2011 = 0.324 K = 0.324 x 1.7 P = 0.5508 P.

Increment = (0.5508 – 0.354) P / 0.354 P = 55.6 %.

Q2) In each area percentage has been changed for every year. Hence 0.

Q3) Suppose total expenditure in 2011 was A and in 2012 was B.

(0.455 – 0.144) A = 46.65

A = 46.65 / 0.311 = 150.

(0.195 – 0.115) B = 16.

0.08 B = 16.

B = 200,

Increment = (200 – 150)/150 = 33.33%

**Set 2**

A cricket team of 11 players is to be performed from a group of 15 players- A.B,C,D,E,F,G,H,I,J,K,L,M,N,O. Among the players A,D,K,L,M,N and O are batsman ;B,C,E,F,G and H are bowlers; I and J are wicketkeepers. It is also known that.

I. The team must have at least 5 batsmen and exactly 1 wicketkeeper.

II. H can be selected only if B is selected.

III. F can be selected only if both G and N are selected.

IV. If I is selected, then F is also selected.

V. K and M cannot be selected together for the team. The same is true for B and G.

Q1) In how many ways can the team be formed?

a) 3

b) 4

c) 5

d) 6

Q2) If G is one of the bowlers in the team, then who will be the wicketkeeper?

a) J

b) I

c) Either a or b

d) No such team is possible

Q.3) If H is selected, then who among the following cannot be selected in the team ?

a) O

b) N

c) G

d) J

Solution :

B and G cannot be together in team.

Case I : When B is selected

F cannot be selected because he can only be selected when B and G will be selected.

Hence team comprises 4 bowlers.

Bowlers :- B,H,C,E

Batsman :- A,D,L,O,K/M

Wicket-keeper :- J.

Combination :- 2 x 1 x 1 = 2.

Case II :- When G is selected

H cannot be selected.

Batsman :- A,D,L,O,K/M

Bowlers :- G,F,C,E

Wicket-keeper :- I/J

Ways = 2 x 1 x 2 = 4.

Case III :- When B and G both are not selected.

Then there is no such combination possible.

Answer 1) 2+4 = 6.

Answer 2) I/J hence option C

Answer 3) G.

**Set 3**

The Total sales revenue of a company and expenditure are given in 4 quarters Q1, Q2, Q3 and Q4.

Quarter | Total sales Revenue(in lakh) | Expenditure(in lakh) |
---|---|---|

Q1 | 75 | 50 |

Q2 | 80 | 60 |

Q3 | 70 | 40 |

Q4 | 85 | 60 |

The tax paid by the company in 4 quarters as the percentage of total sales revenue in 4 quarters are 18%, 12%,15% and 20% respectively.

Net sales = total sales revenue – taxes.

Profit is excess of net sales over expenditure.

Profitability = profit / net sales.

Q1) In which quarter profitability of company was highest?

Q2) What is the percentage decrease in the profit made by the company from Q1 to Q4 ?

Q3) How much money company paid as tax in total ?

Firstly we need to find net sales and taxes.

Then profit and profitability also can find.

Tax = tax% x total sales.

Net sales = total sales – tax

Profit = net sales – expenditure.

Profitability = profit / net sales

Quarter | Tax | Net sales | profit | Profitability |
---|---|---|---|---|

Q1 | 13.5 | 61.5 | 11.5 | 11.5 / 61.5 = 0.17 |

Q2 | 9.6 | 70.4 | 10.4 | 10.4 / 60=0.17 |

Q3 | 10.5 | 59.5 | 19.5 | 19.5 / 40=48.75 |

Q4 | 17 | 68 | 8 | 8/60=13.33 |

Answer 1) Q3

Answer 2) Profit made by Q1 = 11.5

Profit made by Q4 = 8

Decrement = 11.5 – 8 / 11.5 = 30.43%

Answer 3) 50.6 lakh rupees.

The table given below shows the percentage break-up of the Gross Domestic Expenditure on four areas - Basic

Research (BR), Applied Research (AR), Experimental Development Research (EDR) and Miscellaneous Research (MR) – of Research and Development (R&D) activity by a country in the period 2008-12.

R & D | 2008 | 2009 | 2010 | 2011 | 2012 |
---|---|---|---|---|---|

BR | 10.7 | 15 | 30.5 | 45.5 | 19.5 |

AR | 22.8 | 20.6 | 20.4 | 14.4 | 11.5 |

EDR | 62 | 55.4 | 35.4 | 32.4 | 64.2 |

MR | 4.5 | 9 | 13.7 | 7.7 | 4.8 |

Q1. If the expenditure on AR in 2011 was 20% more than that in 2010, then by what percent was the expenditure on EDR in 2011 more than that in 2010?

a) 55.6

b) 50.4

c) 66.5

d) 45.8

Q2. If the expenditure on R&D was equal in all the years during the given period, then how many areas witnessed a continual increase in expenditure during the given period?

a) 3

b) 1

c) 2

d) 0

Q3. If the absolute difference between the expenditures on BR and AR in 2011 was $46.65 mn and that in 2012 was$16 mn, then the total expenditure on R&D in 2012 was what percent more than that in 2011?

a) 25.00

b) 33.33

c) 66.67

d) 35.00

Solution :

Q1) Suppose Total expenditure was P in 2010 and K in 2011.

P (0.204) x 1.2 = K (0.144)

1.7 P = K.

Expenditure on EDR in 2010 = 0.354 P.

Expenditure on EDR in 2011 = 0.324 K = 0.324 x 1.7 P = 0.5508 P.

Increment = (0.5508 – 0.354) P / 0.354 P = 55.6 %.

Q2) In each area percentage has been changed for every year. Hence 0.

Q3) Suppose total expenditure in 2011 was A and in 2012 was B.

(0.455 – 0.144) A = 46.65

A = 46.65 / 0.311 = 150.

(0.195 – 0.115) B = 16.

0.08 B = 16.

B = 200,

Increment = (200 – 150)/150 = 33.33%

**Set 2**

A cricket team of 11 players is to be performed from a group of 15 players- A.B,C,D,E,F,G,H,I,J,K,L,M,N,O. Among the players A,D,K,L,M,N and O are batsman ;B,C,E,F,G and H are bowlers; I and J are wicketkeepers. It is also known that.

I. The team must have at least 5 batsmen and exactly 1 wicketkeeper.

II. H can be selected only if B is selected.

III. F can be selected only if both G and N are selected.

IV. If I is selected, then F is also selected.

V. K and M cannot be selected together for the team. The same is true for B and G.

Q1) In how many ways can the team be formed?

a) 3

b) 4

c) 5

d) 6

Q2) If G is one of the bowlers in the team, then who will be the wicketkeeper?

a) J

b) I

c) Either a or b

d) No such team is possible

Q.3) If H is selected, then who among the following cannot be selected in the team ?

a) O

b) N

c) G

d) J

Solution :

B and G cannot be together in team.

Case I : When B is selected

F cannot be selected because he can only be selected when B and G will be selected.

Hence team comprises 4 bowlers.

Bowlers :- B,H,C,E

Batsman :- A,D,L,O,K/M

Wicket-keeper :- J.

Combination :- 2 x 1 x 1 = 2.

Case II :- When G is selected

H cannot be selected.

Batsman :- A,D,L,O,K/M

Bowlers :- G,F,C,E

Wicket-keeper :- I/J

Ways = 2 x 1 x 2 = 4.

Case III :- When B and G both are not selected.

Then there is no such combination possible.

Answer 1) 2+4 = 6.

Answer 2) I/J hence option C

Answer 3) G.

**Set 3**

The Total sales revenue of a company and expenditure are given in 4 quarters Q1, Q2, Q3 and Q4.

Quarter | Total sales Revenue(in lakh) | Expenditure(in lakh) |
---|---|---|

Q1 | 75 | 50 |

Q2 | 80 | 60 |

Q3 | 70 | 40 |

Q4 | 85 | 60 |

The tax paid by the company in 4 quarters as the percentage of total sales revenue in 4 quarters are 18%, 12%,15% and 20% respectively.

Net sales = total sales revenue – taxes.

Profit is excess of net sales over expenditure.

Profitability = profit / net sales.

Q1) In which quarter profitability of company was highest?

Q2) What is the percentage decrease in the profit made by the company from Q1 to Q4 ?

Q3) How much money company paid as tax in total ?

Firstly we need to find net sales and taxes.

Then profit and profitability also can find.

Tax = tax% x total sales.

Net sales = total sales – tax

Profit = net sales – expenditure.

Profitability = profit / net sales

Quarter | Tax | Net sales | profit | Profitability |
---|---|---|---|---|

Q1 | 13.5 | 61.5 | 11.5 | 11.5 / 61.5 = 0.17 |

Q2 | 9.6 | 70.4 | 10.4 | 10.4 / 60=0.17 |

Q3 | 10.5 | 59.5 | 19.5 | 19.5 / 40=48.75 |

Q4 | 17 | 68 | 8 | 8/60=13.33 |

Answer 1) Q3

Answer 2) Profit made by Q1 = 11.5

Profit made by Q4 = 8

Decrement = 11.5 – 8 / 11.5 = 30.43%

Answer 3) 50.6 lakh rupees.