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Question

Mrs Wong sold some cakes to Shops A, B and C. Shop A bough 20% of the cakes. Shop B bought 4 times as many cakes as Shop C. Shop B bought 88 more cakes than Shop A. How many cakes did Mrs Wong sell altogether?

Answer

This is a Branching question. 

   A    B      C    Total   
R1      20u 80u 100u
R2   4 1 5
CR 100u 320u    80u   500u

320u – 100u  = 88

220u = 88

1u = 88 ÷ 220 = 0.4

500u = 500 × 0.4 = 200 cakes

 

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Let amount of cakes shop A bought be 0.2u

Shop B = 0.2u + 88

Shop C = 1/4 (0.2u + 88) = 0.05u + 22

Total amount of cakes = u

u = (0.2u + 88) + (0.05u +22) +0.2u = 0.45u + 110

0.55u = 110 

u = 200

 

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A -> 20%

    = 1/5

      A : B+C                 B : C

       1  :  4                     4 : 1

×5   |      |×5          ×4 |    |×4

      5  :  20                  16   4

 

16u – 5u = 11u

11u = 88

1u  = 8

25u = 25 × 8

        = 200 (Ans)

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cakes bought by Shop —
C : 8 units
B : 8 units x 4 = 32 units

100% – 20% = 80% ——- 8 + 32 = 40 units (cakes bought by Shops B and C)
20% ——- 10 units (cakes bought by Shop A)
32 – 10 = 22
22 units = 88
1 unit = 4
40 + 10 = 50
50 units = 50 x 4 = 200

As : 200 cakes.

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