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Direction : Study the information given below and answer the questions based on it.
There are three highways i.e. Highways A, Highways B and Highways C, Some numbers of vehicles on these highways on different days i.e. Friday, Saturday and Sunday. On each day some numbers of vehicles pass on these three highways.
Friday: The number of vehicles on highway B is one third of the highway B of Saturday. The number of vehicles on highway C is 3/4th of highway C of Saturday. The number of vehicle on highway A and C is same.
Saturday: Total number of vehicle of Saturday is 75000. The number of vehicles on highway B is 15000 less than that of highway A & C together. The number of vehicles on highway A is 5/6th of highway A of Sunday.
Sunday: Total number of vehicles of Sunday is 4/5th of Saturday. The number of vehicle of highway A is equal to highway B of Saturday. The number of vehicles on highway C is same on Saturday and Sunday.
What is the total number of vehicles on Highway A of three days?
75000
65000
60000
70000
80000
Okay, here’s how we crack this:
- Let’s assign variables:
- Friday: A1, B1, C1
- Saturday: A2, B2, C2
- Sunday: A3, B3, C3
- Saturday’s numbers:
- Total vehicles = 75,000
- B2 is 15,000 less than A2 + C2, so B2 = (A2 + C2) - 15,000
- Also, A2 + B2 + C2 = 75,000
- Friday’s rules:
- B1 is ? of B2.
- C1 is ¾ of C2.
- A1 = C1
- Sunday’s rules:
- Total is 4/5 × 75,000 = 60,000
- A3 = B2
- C3 = C2
- A2 = 5/6 A3
So, let’s solve:
1. From Sunday:
A3 + B3 + C3 = 60,000
A3 = B2, C3 = C2
2. From Saturday:
A2 + B2 + C2 = 75,000
B2 = (A2 + C2) - 15,000 (so, A2 + C2 = B2 + 15,000)
Sub into first: (B2 + 15,000) + B2 = 75,000 ? 2B2 + 15,000 = 75,000 ? B2 = 30,000
So, A2 + C2 = 45,000
3. Also, A2 = 5/6 A3.
Since A3 = B2 = 30,000, A2 = 5/6 × 30,000 = 25,000
So, C2 = 45,000 - 25,000 = 20,000
Now, working backwards:
- On Sunday:
A3 = 30,000, C3 = 20,000
So, B3 = 60,000 - 30,000 - 20,000 = 10,000
- On Friday:
B1 = ? × 30,000 = 10,000
C1 = ¾ × 20,000 = 15,000
A1 = C1 = 15,000
- Sum up Highway A: A1 + A2 + A3 = 15,000 + 25,000 + 30,000 = 70,000
? Option 4, 70,000 is correct.
Quick recap:
- Broke everything into variables.
- Used totals and relationships to deduce each value.
- Added up just the A’s.
That’s all there is to it. Option 4 is the answer.
By: Parvesh Mehta ProfileResourcesReport error
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