Ratios (OCR GCSE Maths: Higher)

Here are the ingredients needed to make 12 shortcakes.

Liz makes some shortcakes.
She uses 25 ml of milk.

How many shortcakes does Liz make?

Robert has   

500 g of sugar
1000 g of butter
1000 g of flour
500 ml of milk

Work out the greatest number of shortcakes Robert can make.

Here is a list of ingredients for making 18 mince pies.

Elaine wants to make 45 mince pies.

Elaine has

1 kg of butter
I kg of flour
500 g of sugar
600 g of mincemeat 6 eggs

Does Elaine have enough of each ingredient to make 45 mince pies?
You must show clearly how you got your answer.

Here are the ingredients needed to make 8 shortbread biscuits.

Tariq is going to make some shortbread biscuits.
He has the following ingredients

330g butter    200g caster sugar    450g flour

Work out the greatest number of shortbread biscuits that Tariq can make with his ingredients.
You must show all your working.

160 cm of gold wire has a weight of 17.8 grams.

Work out the weight of 210 cm of the gold wire.

There are 1200 students at a school.

Kate is helping to organise a party.
She is going to order pizza.

Kate takes a sample of 60 of the students at the school.
She asks each student to tell her one type of pizza they want.

The table shows information about her results.

Work out how much ham pizza Kate should order.
Write down any assumption you make and explain how this could affect your answer.

Rob is learning about the planets.

Rob makes a model of the Sun.
He also makes a model of the planet Jupiter.

Rob is going to hang the two models in the school hall.

Rob wants a distance of 16 m between the two models.
The real distance between the planet Jupiter and the Sun is 8 x 10⁸ km

Work out the scale Rob should use.
Give your answer in the form 

The ratio of the number of boys to the number of girls in a school is 4: 5
There are 95 girls in the school.

Work out the total number of students in the school.

5 schools sent some students to a conference.

One of the schools sent both boys and girls.
This school sent 16 boys.
The ratio of the number of boys it sent to the number of girls it sent was 1: 2

The other 4 schools sent only girls.
Each of the 5 schools sent the same number of students.

Work out the total number of students sent to the conference by these 5 schools.

Babajan makes breakfast cereal.
She mixes nuts, raisins and oats in the ratio 3 : 2 : 5 by weight.

On Monday, Babajan uses 60 grams of nuts.

Work out the weight of raisins and the weight of oats she uses to make the breakfast cereal.

On Tuesday, Babajan makes 300 grams of the breakfast cereal.

500 grams of nuts cost £8

Work out the cost of the nuts used to make 300 grams of the breakfast cereal.

Talil is going to make some concrete mix.
He needs to mix cement, sand and gravel in the ratio 1 : 3 : 5 by weight.

Talil wants to make 180 kg of concrete mix.

Talil has

15 kg of cement
85 kg of sand
100 kg of gravel

Does Talil have enough cement, sand and gravel to make the concrete mix?

Emma has a digital photo.

The photo has a width of 720 pixels.
The photo has a height of 540 pixels.

Write down the ratio of the width of the photo to the height of the photo.
Give your ratio in its simplest form.

Emma wants the ratio of the width of the photo to the height of the photo to be 3 : 2
She reduces the number of pixels in the height of the photo.
The width of the photo is still 720 pixels.

The ratio of the width of the photo to the new height of the photo is 3 : 2

Work out the new height of the photo.

Deon needs 50g of sugar to make 15 biscuits.

She also needs
         three times as much flour as sugar
         two times as much butter as sugar

Deon is going to make 60 biscuits.

Work out the amount of flour she needs.

Deon has to buy all the butter she needs to make 60 biscuits.
She buys the butter in 250 g packs.

How many packs of butter does Deon need to buy?

A shop sells packs of black pens, packs of red pens and packs of green pens.

There are

      2 pens in each pack of black pens
      5 pens in each pack of red pens
      6 pens in each pack of green pens

On Monday,

A total of 212 pens were sold.
Work out the number of green pens sold.

George is the manager of a shoe shop.
He samples 50 of his customers and asks them about the one style of shoe they would buy next.
The table shows his results.

George buys 1000 pairs of shoes with the number of each style based on his survey results.
How many pairs of sandals should he buy?
Write down any assumption you make about his sample.

Reece and Sarah share some money in the ratio 9 : 16.

Reece says that Sarah gets more than 60% of this money.

Show that Reece is correct.

Two bags each contain only red counters and yellow counters.

In Bag A, the ratio of red counters to yellow counters is 1 : 4.

In Bag B,  of the counters are red.

i) Sharon says

   The proportion of the counters that are red is the same in both bags.

Explain why Sharon is not correct.

ii) The number of counters in the two bags is the same.

Complete the table below to show how many counters of each colour could be in the bags.

[3]

Brendon, Asha and Julie share some money in the ratios 3 : 2 : 6 The total amount of money that Asha and Julie receive is $36

Work out the amount of money that Brendon receives.

$..................

A plane has a length ofmetres.

A scale model is made of the plane.
The scale of the model is 

Work out the length of the scale model.
Give your answer in centimetres.

A football team played 55 games.

Each game was won, drawn or lost.

number of games won : number of games drawn : number of games lost = 6 : 3 : 2

Work out how many more games the team won than the team lost.

Two wire shapes make an earring.
The shapes are

a circle with radius 21 mm

and

a quarter circle.

Show that the radius of the quarter circle is 6 mm.

White paint costs £2.80 per litre.
Blue paint costs £3.50 per litre.
White paint and blue paint are mixed in the ratio 3 : 2

Work out the cost of 18 litres of the mixture.

£........................

Ed and Fay shared £330 in the ratio    7 : 4

Ed gives Fay some of his money.

Fay now has the same amount as Ed.

How much does Ed give Fay?

£...............................

Colin works on 5 days each week.
Each day he drives from his home to work and from work to his home.

Colin pays £3.50 each day to use the car park at work.

The distance from Colin's home to work is 9 miles.
Colin's car uses one gallon of petrol every 45.2 miles.

   1 litre of petrol costs 136.9p
   1 gallon = 4.546 litres

Work out the total cost for Colin to use his car for work each week.
You must show all your working.

William is building a planetary path for people to walk along. The planetary path will have a model of the Sun and models of the planets.

William uses two different scales.
He uses

   1 cm to 1000 km for the diameter of each planet
   1 m to 1 000 000km for the distance from the Sun to each planet

William makes a model of the planet Venus.
The model has a diameter of 12.1 cm.

Work out the real diameter of the planet Venus.
Give your answer in standard form.

William works out the distance from the model of the Sun to the model of the planet Neptune.

The real distance from the Sun to the planet Neptune is 4.503 10⁹ km.

Work out the distance from the model of the Sun to the model of the planet Neptune.
Give your answer in km, correct to 1 decimal place.

There are some red counters and some yellow counters in a bag in the ratio 1 : 5
There are 20 yellow counters in the bag.

Work out the number of red counters in the bag.

Janet puts some more red counters into the bag.
The ratio of the number of red counters to the number of yellow counters is now 1 : 2

How many red counters does Janet put into the bag?

Frank, Mary and Seth shared some sweets in the ratio 4 : 5 : 7 Seth got 18 more sweets than Frank.

Work out the total number of sweets they shared.

There are some red counters and some yellow counters in a bag. There are 30 yellow counters in the bag.
The ratio of the number of red counters to the number of yellow counters is 1 : 6

Work out the number of red counters in the bag.

Riza puts some more red counters into the bag.
The ratio of the number of red counters to the number of yellow counters is now 1 : 2

How many red counters does Riza put into the bag?

The perimeter of a right-angled triangle is 72 cm.
The lengths of its sides are in the ratio 3 : 4 : 5

Work out the area of the triangle.

The surface gravity of a planet can be worked out using the formula

where

    kilograms is the mass of the planet

    metres is the radius of the planet

For the Earth and Jupiter here are the values of and .

Work out the ratio of the surface gravity of Earth to the surface gravity of Jupiter.
Write your answer in the form 

£360 is shared between Abby, Ben, Chloe and Denesh.

The ratio of the amount Abby gets to the amount Ben gets is 2 : 7

Chloe and Denesh each get 1.5 times the amount Abby gets.

Work out the amount of money that Ben gets.

An interior angle of an isosceles triangle is p° and an exterior angle is q °.

It is given that q = 5p .
Write the ratio p : q in its simplest form.

Work out the two different possible sets of angles for the isosceles triangle.

Triangle 1: ............°, .............°, .............° Triangle 2: ............°, .............°, .............°

Sundip and Emma have some money.
The ratio of Sundip’s money to Emma’s money is 3 : 5.
Emma spends £450 of her money.
The ratio of Sundip’s money to Emma’s money is now 2 : 3.

Find how much money Sundip has.

£ ........................................................... 

Bob makes dry concrete by mixing cement, sand and stone in the ratio 1 : 2 : 3 by weight.
He buys the cement, sand and stone in bags as shown in this table.

He packs the dry concrete into 30kg bags.

Bob buys just enough cement, sand and stone to make 50 bags of dry concrete.

Show that Bob buys 500kg of sand.

Bob sells the 50 bags of dry concrete for a total of £396.

Calculate Bob’s percentage profit.

Mariana sells bags of bird food.

The bags that Mariana sold last week each contained 12kg of seeds.

The bags that she is going to sell next week will each contain a mixture of nuts and seeds where for each bag

weight of nuts : weight of seeds = 4 : 5

The total weight of the nuts and the seeds in each bag will be 19.35 kg

The weight of seeds in each bag that Mariana sells next week will be less than the weight of seeds in each bag that Mariana sold last week.

Work out this decrease as a percentage of the weight of seeds in each bag that Mariana sold last week.
Give your answer correct to one decimal place.

....................................................... %

Andreas, Isla and Paulo share some money in the ratios 

The total amount of money that Isla and Paulo receive is  more than the amount of money that Andreas receives.

Andreas buys a video game for  with some of his share of the money.

Work out how much money Andreas has left from his share of the money when he has bought the video game.

£................................................ 

Work out the difference between the largest share and the smallest share when 3450 yen is divided in the ratio 2 : 6 : 7

....................................................... yen 

Circle the correct statement.

Jeff and Kaz share £270 in the ratio Jeff : Kaz = 2.6 : 1

How much more than Kaz does Jeff get?

£ .......................................

The cost of a holiday is £2400

Rana pays a deposit followed by monthly payments, in the ratio

She makes 6 equal monthly payments.

Work out her monthly payment.

 £............................

Work out

cube root of 512 : reciprocal of 0.4

Give your answer in the form : 1

Here is a quadrilateral.

and

Show that .

Use 8 km/h = 5 mph to write a formula for in terms of .

Purple paint is made by mixing red paint and blue paint in the ratio 5 : 2  Yan has 30 litres of red paint and 9 litres of blue paint.

What is the maximum amount of purple paint he can make?

.............................litres 

Theo starts with savings of £18 James starts with no savings.

Each week from now,

   Theo will save £4.50 and James will save £4

In how many weeks will Theo and James have savings in the ratio 15 : 8?

Rana sells 192 cakes in the ratio    small : medium : large    =    7 : 6 : 11

The profit for one medium cake is twice the profit for one small cake.
The profit for one large cake is three times the profit for one small cake.

Her total profit is £532.48

Work out the profit for one small cake.

£..................... 

A factory makes 450 pies every day.
The pies are chicken pies or steak pies.

Each day Milo takes a sample of 15 pies to check.

The proportion of the pies in his sample that are chicken is the same as the proportion of the pies made that day that are chicken.

On Monday Milo calculated that he needed exactly 4 chicken pies in his sample.

Work out the total number of chicken pies that were made on Monday.

On Tuesday, the number of steak pies Milo needs in his sample is 6 correct to the nearest whole number.

Milo takes at random a pie from the 450 pies made on Tuesday.

Work out the lower bound of the probability that the pie is a steak pie.

Each day a company posts some small letters and some large letters.

The company posts all the letters by first class post.

The tables show information about the cost of sending a small letter by first class post and the cost of sending a large letter by first class post.

Small Letter

Large Letter

One day the company wants to post 200 letters.

The ratio of the number of small letters to the number of large letters is 3 :2

70% of the large letters weigh 0—100 g.

The rest of the large letters weigh 101—250 g.

Work out the total cost of posting the 200 letters by first class post.

The diagram shows a cylinder and a cone.

The cylinder has radius 2cm and height 9cm.
The cone has radius cm and height cm.

The ratio  is 1 : 4.
The volume of the cone is equal to the volume of the cylinder.

Work out the value of .

[The volume of a cone with radius and height is ]

The prices of two phones are in the ratio x : y.

When the prices are both increased by £20, the ratio becomes 5 : 2.
When the prices are both reduced by £5, the ratio becomes 5 : 1.

Express the ratio x : y in its lowest terms.

Danil, Gabriel and Hadley share some money in the ratios 3 : 5 : 9 The difference between the amount of money that Gabriel receives and the amount of money that Hadley receives is 196 euros.

Work out the amount of money that Danil receives.

...................................................... euros

There are some red counters and some yellow counters in a bag. There are 30 yellow counters in the bag.
The ratio of the number of red counters to the number of yellow counters is 1 : 6

Work out the number of red counters in the bag.

Riza puts some more red counters into the bag.
The ratio of the number of red counters to the number of yellow counters is now 1 : 2

How many red counters does Riza put into the bag?

Frank, Mary and Seth shared some sweets in the ratio 4 : 5 : 7
Seth got 18 more sweets than Frank.

Work out the total number of sweets they shared.

The perimeter of a right-angled triangle is 72 cm.
The lengths of its sides are in the ratio 3 : 4 : 5

Work out the area of the triangle.

The surface gravity of a planet can be worked out using the formula

where

 kilograms is the mass of the planet metres is the radius of the planet

For the Earth and Jupiter here are the values of  and .

Work out the ratio of the surface gravity of Earth to the surface gravity of Jupiter.
Write your answer in the form 1 : 

Circle the correct statement.

Jeff and Kaz share £270 in the ratio Jeff : Kaz = 2.6 : 1

How much more than Kaz does Jeff get?

£ .......................................

The cost of a holiday is £2400

Rana pays a deposit followed by monthly payments, in the ratio

She makes 6 equal monthly payments.

Work out her monthly payment.

 £............................

Work out

cube root of 512 : reciprocal of 0.4

Give your answer in the form : 1

Here is a quadrilateral.

and

Show that