Arun Sharma Solutions for Exercise 2: Review Test

A car after traveling 18 km from a point A developed some problem in the engine and the speed $4/5th$ of its original speed. As a result, the car reached point$B 45 minutes$  late. If the engine had developed the same problem after $30 km from A,$then it would have reached B only 36 minutes late. The original speed of the car (in km per hour) and the distance between the points A and B (in km) are 

Mr. and Mrs. Shalf travel from City $\mathrm{A}$to City $\mathrm{B}$and break journey at City $\mathrm{C}$in between. Somewhere between City $\mathrm{A}$and City $\mathrm{C}$, Mrs. Shah asks "How far have we travelled?" Mr.-Shah replies. "Half as far as the distance from here to city $\mathrm{C}$". Somewhere between City $\mathrm{C}$and City $\mathrm{B}$, exactly $200 \mathrm{km}$from the point where she asked the first question, Mrs. Shah asks "How far do we have to go?" Mr. Shah replies "Half as far as the distance from City $\mathrm{C}$to here. The distance between Cities $\mathrm{A}$and $\mathrm{B}$in$\mathrm{km}$. is

KachuaBhaiya started to move from point $\mathrm{B}$towards point A exactly an hour after Jiggly Pup started from $\mathrm{A}$in the opposite direction. KachuaBhaiyas’s speed was twice that of Jiggly Pup. When Jiggly Pup had covered one-sixth of the distance between the points $\mathrm{A}$and $\mathrm{B}$. KachuaBhaiya had also covered the same distance.

How many more hours would Jiggly Pup (comparedTo KachuaBhaiya) take to complete his journey?

A group of workers was put on a publishing job. From the second day onwards one worker was with drawn each day. The job was finished when the last worker was withdrawn. Had no worker been with drawn at any stage, the group would have finished I the job in two-thirds the time. How many workers were there in the group?

A ship leaves on a long voyage. When it is $18 \mathrm{miles}$ from the shore, a seaplane, whose speed is ten times that of the ship, is sent to deliver mail. How far from the shore does the seaplane catch up with the ship?

One man can do as a woman can do in $2$ days. A child does one-third the work in a day as a woman. If an estate-owner hires $39$pairs of hands, men, women and children in the ratio $6:5:2$and pays them in all $1113$at the end of days work, what must the daily wages of a child be, if the wages are proportional to the amount of work done?

A water tank has three taps $\mathrm{A}, \mathrm{B} \mathrm{and} \mathrm{C}.$ $\mathrm{A}$fills four buckets in $24$mins, $\mathrm{B}$fills $8$buckets in $1 \mathrm{hour}$and $\mathrm{C}$fills $2$ buckets in $20$minutes. If all the taps are opened together a full tank is emptied in $2$hours. If a bucket can hold $5 \mathrm{litres}$ of water, what is the capacity of the tank?

A man buys spirit at $60 \mathrm{per} \mathrm{litre}$, adds water to it and then sells it at$75 \mathrm{per} \mathrm{litre}$. What is the ratio of spirit to water if his profit in the deal is $37.5\%$?