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 in all the three days 246 more than total number of products sold by shop C and E on Monday together. If total number of products sold by A on Monday and Wednesday is equal, then find the ratio of ‘x’ to ‘y’.

  1. A.

    16: 73

  2. B.

    17: 25

  3. C.

    16: 75

  4. D.

    18: 77

  5. E.

    None of these

Attempted by 2 students.

Show answer & explanation

Correct answer: C

Concept

In a data-interpretation grid, every shop's three-day total equals Monday + Tuesday + Wednesday. When a column gives the Monday:Tuesday ratio and the Tuesday figure, Monday is fixed by that ratio; when a column gives Wednesday as a percentage of the three-day total, the total satisfies Total = Monday + Tuesday + (percent x Total), which you solve for the total. Two given conditions then pin the unknown multipliers.

Step-by-step working

  1. Shop C: Monday:Tuesday = 4:5 and Tuesday = 10x, so Monday = (4/5) x 10x = 8x. Wednesday is 20% of C's total, so Total_C = 8x + 10x + 0.20 x Total_C, giving 0.80 x Total_C = 18x and Total_C = 22.5x.

  2. Shop E: Monday:Tuesday = 3:4 and Tuesday = 15x, so Monday = (3/4) x 15x = 11.25x. Wednesday is 30% of E's total, so Total_E = 11.25x + 15x + 0.30 x Total_E, giving 0.70 x Total_E = 26.25x and Total_E = 37.5x.

  3. Apply Note (i): the difference of the three-day totals of C and E is 120, so 37.5x - 22.5x = 15x = 120, hence x = 8.

  4. Monday sales: Monday_C = 8x = 64 and Monday_E = 11.25x = 90, so C and E together sold 64 + 90 = 154 on Monday.

  5. Stem condition 1: A's three-day total is 246 more than (Monday_C + Monday_E), so Total_A = 154 + 246 = 400.

  6. A's Tuesday = (25/2)x = 12.5 x 8 = 100. Stem condition 2 says A's Monday equals A's Wednesday; call each W. Then 2W + 100 = 400, so W = 150 — i.e. Monday_A = Wednesday_A = 150.

  7. Wednesday_A is y% of A's three-day total, so y% of 400 = 150, giving y = 150 x 100 / 400 = 37.5.

Cross-check

x = 8 and y = 37.5, so x : y = 8 : 37.5. Multiply both parts by 2 to clear the decimal: 16 : 75. Verifying the totals: Total_C = 22.5 x 8 = 180 and Total_E = 37.5 x 8 = 300, whose difference is 300 - 180 = 120, matching Note (i); and A's parts 150 + 100 + 150 = 400 match Total_A. The required ratio is 16 : 75.

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