GCSE Dividing in a ratio Practice Questions

Free GCSE Dividing in a ratio practice questions with full step-by-step worked solutions. Covers sharing in a ratio, total parts, two-part ratio, whole objects. Practise exam-style problems and check your method.

sharing in a ratiototal partstwo-part ratiowhole objectssmaller sharelengths
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Share £20 between Ali and Beth in the ratio 1:31 : 3. Work out Beth’s share.
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Worked solution

  1. Add the parts of the ratio

    1+3=41 + 3 = 4

    The quantity is split into 44 equal parts altogether.

  2. Find the value of one part

    20÷4=520 \div 4 = 5

    Divide the total by the number of parts: one part is £5\pounds 5.

  3. Work out the share asked for

    3×5=153 \times 5 = 15

    That share is 33 of the 44 parts, so it is £15\pounds 15. Check: 5+15=205 + 15 = 20. ✓\checkmark

Answer
£15\pounds 15
Question 2
2 markseasy
Some money is shared in the ratio 1:31 : 3. The smaller share is £7. Work out the larger share.
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Worked solution

  1. Work out the value of one part

    1 part=£71 \text{ part} = \pounds 7

    The smaller share is exactly 11 part of the ratio, so one part is worth £7\pounds 7.

  2. Multiply up for the larger share

    3×7=213 \times 7 = 21

    The larger share is 33 parts, so it is 3×£7=£213 \times \pounds 7 = \pounds 21.

  3. Check against the ratio

    7:21=1:37 : 21 = 1 : 3

    Dividing both sides by 77 gives 1:31 : 3, which matches the question. ✓\checkmark

Answer
£21\pounds 21
Question 3
2 marksintermediate
Priya shares £150 between three people in the ratio 1:2:21 : 2 : 2. She says, “The two equal shares must be £75 each, because £150 divided by 22 is £75.” Explain why Priya is wrong.
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Worked solution

  1. Count the parts

    1+2+2=51 + 2 + 2 = 5

    The £150 is shared into 55 equal parts, not into 22 shares.

  2. Find one part

    150÷5=30150 \div 5 = 30

    One part is worth £30\pounds 30.

  3. Work out the three shares

    1×30=30,2×30=60,2×30=601 \times 30 = 30, \quad 2 \times 30 = 60, \quad 2 \times 30 = 60

    The shares are £30, £60 and £60.

  4. Check they add back to the total

    30+60+60=15030 + 60 + 60 = 150

    The three shares total £150. ✓\checkmark

  5. Show why Priya’s answer cannot work

    75+75=15075 + 75 = 150

    If the two equal shares were £75 each they would use up ALL the money, leaving nothing for the third person.

  6. State the correct shares

    £30, £60, £60\pounds 30, \ \pounds 60, \ \pounds 60

    The two equal shares are £60\pounds 60 each, not £75\pounds 75.

Answer
£60 each, not £75\pounds 60 \text{ each, not } \pounds 75
Question 4
3 markshard
Jo and Sam share some sweets in the ratio 5:25 : 2. Jo receives 2424 more sweets than Sam. How many sweets were shared altogether?
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Worked solution

  1. Draw the two bars

    Jo=5 parts,Sam=2 parts\text{Jo} = 5 \text{ parts}, \quad \text{Sam} = 2 \text{ parts}

    Jo’s bar is 55 blocks long, Sam’s is 22 blocks long, and every block is the same size.

  2. Find how many blocks longer Jo’s bar is

    5−2=3 parts5 - 2 = 3 \text{ parts}

    Jo’s bar sticks out by 33 blocks.

  3. Set the extra blocks equal to 24 sweets

    3 parts=24 sweets3 \text{ parts} = 24 \text{ sweets}

    Those 33 extra blocks are the 2424 extra sweets.

  4. Find one part

    24÷3=824 \div 3 = 8

    One block is 88 sweets.

  5. Work out Jo’s sweets

    5×8=405 \times 8 = 40

    Jo has 4040 sweets.

  6. Work out Sam’s sweets

    2×8=162 \times 8 = 16

    Sam has 1616 sweets.

  7. Check the difference

    40−16=2440 - 16 = 24

    Jo has 2424 more sweets than Sam. ✓\checkmark

  8. Work out the total

    40+16=5640 + 16 = 56

    There were 5656 sweets altogether.

  9. Check using the total parts

    (5+2)×8=56(5 + 2) \times 8 = 56

    Seven blocks at 88 sweets each is 5656 — the same answer. ✓\checkmark

  10. Watch the common error

    24÷7 is not a whole number24 \div 7 \text{ is not a whole number}

    Dividing 2424 by the TOTAL parts would treat 2424 as the total number of sweets. It is the DIFFERENCE.

Answer
56 sweets56 \text{ sweets}
Question 5
6 markschallenging
Two numbers are in the ratio 4:74 : 7. When 55 is added to the smaller number and 55 is subtracted from the larger number, the two results are in the ratio 3:43 : 4. Work out the two original numbers.
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Worked solution

  1. Set up the unknown

    k=value of one partk = \text{value of one part}

    The ratio fixes the shape of the numbers but not their size, so introduce one unknown.

  2. Write the two numbers

    smaller=4k,larger=7k\text{smaller} = 4k, \quad \text{larger} = 7k

    Every pair in the ratio 4:74 : 7 has this form.

  3. Apply the change to the smaller number

    4k+54k + 5

    Five is ADDED to the smaller number.

  4. Apply the change to the larger number

    7k−57k - 5

    Five is SUBTRACTED from the larger number — different operations, so read carefully.

  5. Write the new ratio

    (4k+5):(7k−5)=3:4(4k + 5) : (7k - 5) = 3 : 4

    The two results are in the ratio 3:43 : 4.

  6. Turn it into a fraction equation

    4k+57k−5=34\frac{4k + 5}{7k - 5} = \frac{3}{4}

    Equal ratios mean equal fractions.

  7. Cross-multiply

    4(4k+5)=3(7k−5)4(4k + 5) = 3(7k - 5)

    Multiply both sides by 4(7k−5)4(7k - 5).

  8. Expand the left-hand side

    16k+2016k + 20

    Multiply each term inside the bracket by 44.

  9. Expand the right-hand side

    21k−1521k - 15

    Multiply each term by 33. Note that 3×(−5)=−153 \times (-5) = -15.

  10. Write the equation out

    16k+20=21k−1516k + 20 = 21k - 15

    Both sides are now expanded.

  11. Collect the k terms

    20+15=21k−16k20 + 15 = 21k - 16k

    Move the kk terms one way and the numbers the other.

  12. Solve for one part

    35=5k⇒k=735 = 5k \Rightarrow k = 7

    One part is 77.

  13. Work out the two numbers

    4×7=28,7×7=494 \times 7 = 28, \quad 7 \times 7 = 49

    The original numbers are 2828 and 4949.

  14. Check the original ratio

    28:49=4:728 : 49 = 4 : 7

    Dividing both by 77 gives 4:74 : 7. ✓\checkmark

  15. Check the new ratio

    (28+5):(49−5)=33:44=3:4(28 + 5) : (49 - 5) = 33 : 44 = 3 : 4

    Dividing 33:4433 : 44 by 1111 gives 3:43 : 4 — exactly as required. ✓\checkmark

Answer
28 and 4928 \text{ and } 49

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