Irfan is an all-rounder in cricket and is good at all the three aspects of the game – batting, bowling and fielding. For this season, he has assigned himself a weekly training schedule, such that each of the three aspects are practised for exactly three sessions, in a period of 7 days. Also, the gap between any two consecutive practice sessions of any of the three aspects, must not be more than two days. He rests completely on exactly one day of the week and only on Wednesday does he practice all three batting, bowling, fielding. During a certain period of 6 consecutive days, he practised fielding on the first day, batting on the second day, bowling on the third day, fielding on the fourth day, bowling on the fifth day and batting on the sixth day. The above mentioned is only a partial list for some of the days, during which he could have practised more than one of batting, bowling and fielding on the same day.

Q1) the day on which he takes rest is.

Q2) If Irfan practised two of the on the three aspects of the game on a certain day, it can be a day of ?

Q3) Irfan practices which aspect on a Sunday?

**Solution:-**

As per given information table can be implemented

Day | batting | Bowling | Fielding |
---|---|---|---|

1 | Yes | ||

2 | Yes | ||

3 | Yes | ||

4 | Yes | ||

5 | Yes | ||

6 | Yes | ||

7 | - | - | - |

There we can see gap between batting is 3(2nd day & 5th day) and gap between fielding is also 3 (4th day then direct 1st day). it means he does practices all three aspects in between 3rd, 4th and 5th day. If he does practices 5th day he will satisfy all cases. He practices all three aspects on Wednesday. That is 5th day. One day he rests completely. That is 7th day. He does bowling practice also on 1st day or Saturday.

Let’s make a final table.

Day | Batting | Bowling | Fielding |
---|---|---|---|

Saturday | Yes | Yes | |

Sunday | Yes | ||

Monday | Yes | ||

Tuesday | Yes | ||

Wednesday | Yes | Yes | Yes |

Thursday | Yes | ||

Friday | - | - | - |

Answer 1) :- Friday

Answer 2):- Saturday

Answer 3):- Batting.

**Set 2**

A travel agency operates five different buses A,B,C,D,E on a certain route. Since all the five buses are of different types, the capacities (number of seats) of the five buses are all different among 25,30,40,50 and 60 in particular order. The fare per head of each bus is a different among rs 250,300,500,600 and rs 700, in no particular order. It is assumed that for any trip, each bus is fully occupied.

Total revenues per trip for a bus of any type = No of seats x Fare per head.

Further, it is known that for a single trip

- The total revenue collected from bus B is more than that from bus D and the total revenue collected from bus A is more than that from bus E.
- The difference between the fare per head of bus B and that of bus E is rs 200.
- The total revenue collected from each bus is distinct and more than rs 10000.
- The capacity of bus is not 25 and the total revenue collected from bus D is not the least.
- The fare per head of bus C is rs 700 and the total revenue collected from bus D is not rs 15000.

Q1) What is the capacity of bus B ?

Q2) What is the total amount collected per trip from bus A ?

Q3) Which bus gives the second highest total revenue per trip ?

Q4) What is the difference between the total revenue collected per trip from bus D and bus E ?

**Solution**

On the basis of given information,

(i) Revenue of B > D, A > E.

(ii) Fare per head B-E = 200.

(iii) Revenue of each bus is distinct and 10000+

(iv) Capacity of bus not equal to 25 of C.

Not least revenue.

(v) Fare per head of C = 700.

Revenue of D not equal to 15000.

Fare per head of C = 700, B = 500, E =300.

Though revenue of A > E

Hence fare per head of A= 600.

Fare per head of D = 250.

Least revenue should be of D.

Possibilities of revenue

A(600) = 15000,18000,24000,30000,36000.

B(500)=12500,15000,20000,25000,30000.

C(700)=17500,21000,28000,35000,42000.

D(250)=6250,7500,10000,12500,15000.

E(300)=7500,9000,12000,15000,18000.

Least revenue of D is 12500. (250,50)

Revenue of E is 12000.(300,40).

Revenue of A =15000.(600,25).

Revenue of C = 21000.(700,30).

Revenue of B =30000.(500,60).

Ans 1) 60.

Ans 2)15000.

Ans 3)C (21000).

Ans 4) 500.

**Set 3**

A,B,C,D and E cars such that the price of C is twice that of A and the price E is one third of B. The ratio of the price of D and that of C is 4:5.

Q1) How many of the following statements are definitely true or definitely false.

I. The cost of A and E is less than that of B and D together.

II. The cost of D is more than B.

III. The difference between the costs of E and D is more than the difference between the costs A & B.

IV. The ratio of the cost of A to the cost of D is less than 0.6.

Q2) How many of the following statements when considered independently will be sufficient to find the ratio of the cost of A to the of the E ?

I. the difference between the costs of B and C is as same the difference between the costs of A & E.

II. The ratio of the cost of A and that of B is 2:1.

III. The cost of E and D together is equal to the cost of A and B together.

IV. The sum of the costs of B and A together is twice that of C and E together.

Solution (1):-

C = 2A.

5D = 4C.

8A = 4C = 5D.

B = 3E.

By (I) A+E < B+D.

If A=5 then D = 8.

If E =1, B=3.

True.

By (II) D > B.

There is no relation is given in between B & D.

By (III) D – E > A - B

Suppose E = 1, B=3.

If A = 5, D = 8.

True.

By (IV)

A : D < 0.6

False.

Definitely true are I & III.

Solution (II)

By I.

|B – C| = |A – E|.

Not sufficient.

By II.

A : B = 2 : 1.

B = 3E.

A : E = 6 : 1.

Sufficient.

By III,

E + D = A + B

Sufficient

By IV,

A + B = 2(C + E)

Sufficient.

Irfan is an all-rounder in cricket and is good at all the three aspects of the game – batting, bowling and fielding. For this season, he has assigned himself a weekly training schedule, such that each of the three aspects are practised for exactly three sessions, in a period of 7 days. Also, the gap between any two consecutive practice sessions of any of the three aspects, must not be more than two days. He rests completely on exactly one day of the week and only on Wednesday does he practice all three batting, bowling, fielding. During a certain period of 6 consecutive days, he practised fielding on the first day, batting on the second day, bowling on the third day, fielding on the fourth day, bowling on the fifth day and batting on the sixth day. The above mentioned is only a partial list for some of the days, during which he could have practised more than one of batting, bowling and fielding on the same day.

Q1) the day on which he takes rest is.

Q2) If Irfan practised two of the on the three aspects of the game on a certain day, it can be a day of ?

Q3) Irfan practices which aspect on a Sunday?

**Solution:-**

As per given information table can be implemented

Day | batting | Bowling | Fielding |
---|---|---|---|

1 | Yes | ||

2 | Yes | ||

3 | Yes | ||

4 | Yes | ||

5 | Yes | ||

6 | Yes | ||

7 | - | - | - |

There we can see gap between batting is 3(2nd day & 5th day) and gap between fielding is also 3 (4th day then direct 1st day). it means he does practices all three aspects in between 3rd, 4th and 5th day. If he does practices 5th day he will satisfy all cases. He practices all three aspects on Wednesday. That is 5th day. One day he rests completely. That is 7th day. He does bowling practice also on 1st day or Saturday.

Let’s make a final table.

Day | Batting | Bowling | Fielding |
---|---|---|---|

Saturday | Yes | Yes | |

Sunday | Yes | ||

Monday | Yes | ||

Tuesday | Yes | ||

Wednesday | Yes | Yes | Yes |

Thursday | Yes | ||

Friday | - | - | - |

Answer 1) :- Friday

Answer 2):- Saturday

Answer 3):- Batting.

**Set 2**

A travel agency operates five different buses A,B,C,D,E on a certain route. Since all the five buses are of different types, the capacities (number of seats) of the five buses are all different among 25,30,40,50 and 60 in particular order. The fare per head of each bus is a different among rs 250,300,500,600 and rs 700, in no particular order. It is assumed that for any trip, each bus is fully occupied.

Total revenues per trip for a bus of any type = No of seats x Fare per head.

Further, it is known that for a single trip

- The total revenue collected from bus B is more than that from bus D and the total revenue collected from bus A is more than that from bus E.
- The difference between the fare per head of bus B and that of bus E is rs 200.
- The total revenue collected from each bus is distinct and more than rs 10000.
- The capacity of bus is not 25 and the total revenue collected from bus D is not the least.
- The fare per head of bus C is rs 700 and the total revenue collected from bus D is not rs 15000.

Q1) What is the capacity of bus B ?

Q2) What is the total amount collected per trip from bus A ?

Q3) Which bus gives the second highest total revenue per trip ?

Q4) What is the difference between the total revenue collected per trip from bus D and bus E ?

**Solution**

On the basis of given information,

(i) Revenue of B > D, A > E.

(ii) Fare per head B-E = 200.

(iii) Revenue of each bus is distinct and 10000+

(iv) Capacity of bus not equal to 25 of C.

Not least revenue.

(v) Fare per head of C = 700.

Revenue of D not equal to 15000.

Fare per head of C = 700, B = 500, E =300.

Though revenue of A > E

Hence fare per head of A= 600.

Fare per head of D = 250.

Least revenue should be of D.

Possibilities of revenue

A(600) = 15000,18000,24000,30000,36000.

B(500)=12500,15000,20000,25000,30000.

C(700)=17500,21000,28000,35000,42000.

D(250)=6250,7500,10000,12500,15000.

E(300)=7500,9000,12000,15000,18000.

Least revenue of D is 12500. (250,50)

Revenue of E is 12000.(300,40).

Revenue of A =15000.(600,25).

Revenue of C = 21000.(700,30).

Revenue of B =30000.(500,60).

Ans 1) 60.

Ans 2)15000.

Ans 3)C (21000).

Ans 4) 500.

**Set 3**

A,B,C,D and E cars such that the price of C is twice that of A and the price E is one third of B. The ratio of the price of D and that of C is 4:5.

Q1) How many of the following statements are definitely true or definitely false.

I. The cost of A and E is less than that of B and D together.

II. The cost of D is more than B.

III. The difference between the costs of E and D is more than the difference between the costs A & B.

IV. The ratio of the cost of A to the cost of D is less than 0.6.

Q2) How many of the following statements when considered independently will be sufficient to find the ratio of the cost of A to the of the E ?

I. the difference between the costs of B and C is as same the difference between the costs of A & E.

II. The ratio of the cost of A and that of B is 2:1.

III. The cost of E and D together is equal to the cost of A and B together.

IV. The sum of the costs of B and A together is twice that of C and E together.

Solution (1):-

C = 2A.

5D = 4C.

8A = 4C = 5D.

B = 3E.

By (I) A+E < B+D.

If A=5 then D = 8.

If E =1, B=3.

True.

By (II) D > B.

There is no relation is given in between B & D.

By (III) D – E > A - B

Suppose E = 1, B=3.

If A = 5, D = 8.

True.

By (IV)

A : D < 0.6

False.

Definitely true are I & III.

Solution (II)

By I.

|B – C| = |A – E|.

Not sufficient.

By II.

A : B = 2 : 1.

B = 3E.

A : E = 6 : 1.

Sufficient.

By III,

E + D = A + B

Sufficient

By IV,

A + B = 2(C + E)

Sufficient.

There are two things which we have to remember in that set

- Irfan has to practice all three aspects on a particular day.
- Three should not be gap of more than two days.

Now coming to your doubt.. among 3rd,4th and 5th day is the day where he practices all three aspects. If he does practices on 4th day then the gap between fielding is 3 days. Same case with 3rd day also. 5th day is the day which is satisfying above cases. Hence 5th day is Wednesday.

I hope it's clear now.

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