T.S.Jain Solutions for Exercise 1: EXERCISE 5

The average of the first three numbers is double of the fourth number. If the average of all the four numbers is $12$, find the $4^{th}$ number.

Anil took $4$ tests during first year, his average on them was$76$. He took $3$tests during the second year, his average on them was $81$. What was his over all average for both years ?

A cyclist rides $24$ km at $16$ km per hour and a further $36$ km at $15$ km per hour. Find his average speed for the journey?

A certain factory employed $600$ men and $400$ women and the average wage was $₹2.55$ per day. If a woman got $50$ paisa less than a man, what were their daily wages?

If a train maintains an average speed of $40$ km an hour, it arrives at its destination punctually. If however, the average speed is $35$ km an hour, it arrives $15$ minutes late. Find the length of the journey in km.

The average weight of three men $A, B$, and $C$ is $84 kg$ and fourth man $D$ joins them, the average weight of the four becomes $80 kg$. If $E$, whose weight is $3 kg$ more than $D$, replaces $A$, then the average weight of $B, C, D$, and E becomes $79 kg$. Find the weight of $A$.

A man walks from P to Q at the rate of $5$ km an hour and returns from Q to P at the rate of $3$ km an hour. What is the average rate in km per hour for the whole journey ?

A ship, $40 km$ from shore, springs a leak which admits $3\frac{3}{4}$ quintals of water in $12$ minutes. $60$ quintals would suffice to sink the ship, but its pump can throw out $12$ quintals of water in one hour. Find the average rate of sailing so that it may reach the shore just as it begins to sink (in km/hr).