Ratio, Proportion & Partnership • Topic 3 of 4

Dividing in a Ratio

Many SSC sums add or change one part of a ratio. Convert the ratio to actual parts with a multiplier, apply the change, and re-read the new ratio. When a quantity is added equally to all parts, the ratio changes; when one part is changed, set up the new equality. Coins/notes problems (a:b:c counts with different denominations) are ratio plus weighting.

✅ Solved examples

1. A sum of 1100 is divided among A, B, C as 2:3:6. Find C share.
11x = 1100 -> x = 100. C = 6x = 600.
2. Two numbers 3:5; if 8 is added to each they become 2:3. Find them.
(3x+8)/(5x+8) = 2/3 -> 9x+24 = 10x+16 -> x = 8. Numbers 24 and 40.
3. A bag has 1-rupee, 2-rupee and 5-rupee coins in the ratio 3:2:1, with a total value of 96 rupees. Find the number of 2-rupee coins.
Counts 3x, 2x, x. Value = 3x(1) + 2x(2) + x(5) = 3x + 4x + 5x = 12x = 96 -> x = 8. So 2-rupee coins = 2x = 16.
4. Incomes are in ratio 5:4 and expenditures in ratio 3:2. If each saves 6000, find the incomes.
Incomes 5k, 4k; expenditures 3m, 2m. 5k - 3m = 6000 and 4k - 2m = 6000. From the second, 2k - m = 3000 -> m = 2k - 3000. Substitute: 5k - 3(2k - 3000) = 6000 -> 5k - 6k + 9000 = 6000 -> k = 3000. Incomes = 15000 and 12000.

✏️ Practice — try these, take hints as needed

1. Divide 6300 among A,B,C as 1:3:5. B share?
9x = 6300.
x = 700.
3x.
2100
2. Ratio 2:3; add 5 to each -> 3:4. Find numbers.
(2x+5)/(3x+5)=3/4.
8x+20 = 9x+15.
x = 5.
10 and 15
3. Ratio 5:7; subtract 4 from each -> 1:2. Find them.
(5x-4)/(7x-4)=1/2.
10x-8 = 7x-4.
3x = 4 -> x = 4/3.
20/3 and 28/3 (i.e. 6.67 and 9.33)
4. Divide 880 in ratio 1/2 : 1/3 : 1/4.
LCM 12 -> 6:4:3.
13x = 880? -> x not integer; ratio 6:4:3 sum 13.
880/13 each unit.
shares in 6:4:3 (approx 406, 271, 203)
5. A:B = 3:4 and total 4900. A share?
7x = 4900.
x = 700.
3x.
2100

📝 Topic test — 8 questions

Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.

Loading questions…
← Proportion & Variation Partnership & Profit Sharing →