The sum of the incomes of $A$ and $B$ is more than that of $C$ and $D$ taken together. The sum of incomes of $A$ and $C$ is the same as that of $B$ and $D$ taken together. Moreover,$A$ earns half as much as the sum of the incomes of $B$ and $D$. If $A$'s income is $Rs\, 80,000$ per annum and the difference between the income of $B$ and $D$ is the same as $A$'s income,what is $B$'s income?

$A$ is elder to $B$ while $C$ and $D$ are elder to $E$ who lies between $A$ and $C$. If $C$ is elder to $B$,which one of the following statements is necessarily true?

Six persons $A, B, C, D, E,$ and $F$ are standing in a circle. $B$ is between $D$ and $C$. $A$ is between $E$ and $C$. $F$ is to the right of $D$. Who is between $A$ and $F$?

Four young men Raj,Prem,Ved,and Ashok are friendly with four girls Sushma,Kusum,Vimla,and Poonam. Sushma and Vimla are friends. Ved's girlfriend does not like Sushma and Vimla. Kusum does not care for Ved. Prem's girlfriend is friendly with Sushma. Sushma does not like Raj. Who does not like Sushma and Vimla?

There are five persons $P, Q, R, S$ and $T$. One is a football player,one is a chess player,and one is a hockey player. $P$ and $S$ are unmarried ladies and do not participate in any game. None of the ladies plays chess or football. There is a married couple in which $T$ is the husband. $Q$ is the brother of $R$ and is neither a chess player nor a hockey player. Who is the football player?

$(i)$ Five friends $P, Q, R, S$ and $T$ travelled to five different cities of Chennai,Calcutta,Delhi,Bangalore and Hyderabad by five different modes of transport of Bus,Train,Aeroplane,Car and Boat from Mumbai.
$(ii)$ The person who travelled to Delhi did not travel by boat.
$(iii)$ $R$ went to Bangalore by car and $Q$ went to Calcutta by aeroplane.
$(iv)$ $S$ travelled by boat whereas $T$ travelled by train.
$(v)$ Mumbai is not connected by bus to Delhi and Chennai.
Which of the following combinations of person and mode is not correct?