Reasoning 1: Word problems

A box contains a mixture of red and black balls.

There are 800 balls in total.

There are 80 more black balls than red balls.

How many red balls are there in the box?

When a glass is empty it weighs 600 g and when it is half full it weighs 930 g. How much does the glass weigh when it is full?

Give your answer in grams.

A farmhouse shelters 16 animals.

Some of them are chickens and the others are cows.

Altogether these animals have 60 legs.

How many chickens and how many cows are in the farmhouse?

If two apples weigh the same as an orange, and three oranges weigh the same as four lemons, how many apples will weigh the same as 24 lemons?

A class of 195 students went on a field trip.

They took 7 vehicles, some are cars and some are buses.

A car holds 5 students and a bus holds 45 students.

Find the number of cars and the number of buses.

Five years ago, Joe’s age was ¹/₉ of his mother’s.

If Joe is 8 years old now, what is his mother’s present age?

Sarah has £10 more than Callum.

Callum has £3.50 more than Eleanor.

Altogether they have £26.30.

How much money does each one have?

5 p, 2 p and 1 p coins (or a mixture of any of these) are used to make up a total 13 p.

1.      1 x 5p + 3 x 2p + 2 x 1p = 13p

In how many different ways can this be done?

Five teams play in a football competition.

Each team plays each other team only once.

How many matches are there?

There are 40 bedrooms in a hospital ward numbered from 1 to 40.

The maintenance man goes to buy separate metal numerals to put on the doors.

For example, bedroom 27 will need a “2” and a “7”.

How many 3’s will he need to buy to complete the job?

How many posts are needed for 50 metres of fencing if one post is placed every 2 metres?