## Profit & loss, average, Time and Work

Aptitude Solved Problems

Questions :

1. Profit earned by selling an book for Rs. 1450 is same as the loss incurred by selling the book for Rs. 1280. What is the cost price of the book?

2. A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. Find the capacity of the tank (in litres) ?

3. The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 4 : 5 : 6, find the price of the cheapest item?

4. Present ages of Siva and Arun are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively, What is Arun′s present age?

1. Rs. 1365.

2. 5760 litres.

3. Rs. 12000.

4. 24 years.

1. Explanation:

Let Cost price = X.
According to the given data,
( 1450 – x ) = ( x – 1280 )
( 1450 + 1280 ) = ( x + x )
2730 = 2x
x = ( 2730 / 2 )
x = Rs. 1365

∴ The cost price of the book is Rs. 1365.

2. Explanation:

Work done by the inlet in 1 hour = ( 1 / 6) – ( 1 / 8 )
= ( 4 – 3 ) / 24
= 1 / 24
Work done by inlet in 1 min = ( 1 / 24 ) * ( 1 / 60 )
= ( 1 / 1440 )
Volume of ( 1 / 1440 ) part = 4 liters
Volume of whole = ( 1440 * 4 ) litres
= 5760 litres

∴ The capacity of the tank is 5760 litres.

3. Explanation:

Let their prices be 4x, 5x and 6x.
Average of the furnitures = Rs. 15000
( 4x + 5x + 6x ) / 3 = 15000
4x + 5x + 6x = 15000 * 3
15x = ( 15000 * 3 )
x = ( 15000 * 3 ) / 15
x = 1000 * 3
x = Rs. 3000
Cost of cheapest item = 4x
= 4 * 3000
= Rs. 12000

∴ The price of the cheapest item is Rs. 12000.

4. Explanation:

Let the present ages of Siva and Arun be 5x years and 4x years respectively.
Then, ( 5x + 3 ) / ( 4x + 3 ) = ( 11 / 9 )
9 * ( 5x + 3 ) = 11 * ( 4x + 3 )
( 45x + 27 ) = 44x + 33
( 45x – 44x ) = ( 33 – 27 )
x = 6
Arun′s present age = 4x
= 4 * 6
= 24 years

∴ Arun′s present age is 24 years.