Directions: The table given below shows information about total number…

2023

Directions: The table given below shows information about total number products sold by five shops (A, B, C, D and E) on three (Monday + Tuesday + Wednesday) days. Read the data carefully and answer the questions.

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Note: (i) The difference between total number of products sold by C and E in all three days is 120.
(ii) Total products sold by D in all three day is 120.
(iii) Some data are missing, calculate the data if required.

Total number of products sold by shop A on Monday is two times of the total products sold by E on that day and total products sold by A on all three days is 350. Find the ratio of total product sold by C to D on Wednesday.

  1. A.

    5 : 6

  2. B.

    2 : 1

  3. C.

    3 : 4

  4. D.

    1 : 2

  5. E.

    2 : 3

Attempted by 1 students.

Show answer & explanation

Correct answer: B

Concept

In a data-interpretation table built on a single variable, first express every cell in terms of that variable using the given ratios and percentages, then use the numeric anchor conditions (here the difference and total notes) to solve for the variable. The key identity for a part-stated-as-percent-of-total is: if Wednesday is p% of the three-day total, then Monday+Tuesday together are (100 - p)% of that total.

Setting up in terms of x and y

  1. Shop E: Monday : Tuesday = 3 : 4 and Tuesday = 15x, so E(Mon) = (3/4)(15x) = 45/4 x = 11.25x.

  2. Stem: A(Mon) = 2 x E(Mon) = 22.5x. Given A(Tue) = 12.5x, so A's Monday : Tuesday = 22.5x : 12.5x = 9 : 5.

  3. Shop C: Monday : Tuesday = 4 : 5 and Tuesday = 10x, so C(Mon) = 8x; C(Mon)+C(Tue) = 18x.

Finding x from the difference note

  1. C(Wed) is 20% of C's total, so Mon+Tue = 80% of total: 18x = 0.8 x C(total), giving C(total) = 22.5x.

  2. E(Wed) is 30% of E's total, so Mon+Tue = 70% of total. E(Mon)+E(Tue) = 11.25x + 15x = 26.25x = 0.7 x E(total), giving E(total) = 37.5x.

  3. Note (i): |C(total) - E(total)| = 120, i.e. |22.5x - 37.5x| = 15x = 120, so x = 8.

Finding y from shop A

  1. A(Mon)+A(Tue) = 22.5x + 12.5x = 35x = 280 (using x = 8). A's three-day total = 350, so A(Wed) = 70.

  2. A(Wed) is y% of 350, so 350 x (y/100) = 70, giving y = 20.

Computing the required cells

  1. C(Wed) = 20% of C(total) = 0.20 x 22.5x = 4.5x = 4.5 x 8 = 36.

  2. Shop D: three-day total = 120 (note ii). D(Wed) = (y - 5)% = 15% of 120 = 18.

Result

C(Wed) : D(Wed) = 36 : 18 = 2 : 1.

Cross-check

Reconstruct A: Monday 180 + Tuesday 100 + Wednesday 70 = 350, matching the given three-day total, which confirms x = 8 and y = 20 are consistent.

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