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.
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.
The difference between total products sold by B on Monday and Tuesday is 15 and Shop B sold 20% of total products on Tuesday out of total products sold on all three days. Find total number of products sold by E on Wednesday are what percent of total number of products sold by shop B on Wednesday.
- A.
48%
- B.
30%
- C.
36%
- D.
24%
- E.
12%
Show answer & explanation
Correct answer: D
Concept
In a data-interpretation set with a single unknown multiplier, the special conditions (here the C–E total difference) pin that multiplier to one value. Once it is fixed, every shop's day-wise figures follow by two rules: (a) if a shop sells a fixed percentage p of its three-day total on one day, then total = (that day's value) ÷ p; and (b) the three days add up to the total, so the third day = total − (sum of the other two). A ratio a:b means the two parts differ by (b−a) of one share, so a known difference fixes the share size.
Step 1 — Fix the multiplier x from the C–E condition
For C: Tuesday = 10x, and Monday : Tuesday = 4 : 5, so Monday = (4/5)×10x = 8x. Wednesday is 20% of C's total, so total×(1−0.20) = 8x + 10x, giving total C = 18x ÷ 0.80 = 22.5x.
For E: Tuesday = 15x, and Monday : Tuesday = 3 : 4, so Monday = (3/4)×15x = 11.25x. Wednesday is 30% of E's total, so total×(1−0.30) = 11.25x + 15x, giving total E = 26.25x ÷ 0.70 = 37.5x.
Condition (i): | total C − total E | = |22.5x − 37.5x| = 15x = 120, so x = 8.
Step 2 — Wednesday sales of E
Total E = 37.5 × 8 = 300.
E sold on Wednesday = 30% of 300 = 90.
Step 3 — Wednesday sales of B
Monday : Tuesday for B = 7 : x = 7 : 8, so the two parts differ by 1 share; the stated Monday–Tuesday difference of 15 makes 1 share = 15.
Monday B = 7×15 = 105 and Tuesday B = 8×15 = 120.
Tuesday is 20% of B's three-day total, so total B = 120 ÷ 0.20 = 600.
Wednesday B = total − Monday − Tuesday = 600 − 105 − 120 = 375.
Step 4 — Required percentage
E's Wednesday as a percentage of B's Wednesday = (90 ÷ 375) × 100 = 24%.
Cross-check
Totals: C = 22.5×8 = 180, E = 37.5×8 = 300, and 300 − 180 = 120 — matches condition (i).
B totals: 105 + 120 + 375 = 600, and Tuesday 120 is exactly 20% of 600 — consistent.
90/375 reduces to 6/25 = 0.24, confirming 24%.