Aptitude
1 sections, 10 questions
A shopkeeper sells an item at a 15% loss. If he had sold it for ₹180 more, he would have made a profit of 10%. Find the cost price of the item.
Let CP = x
SP at 15% loss = 0.85x
SP at 10% profit = 1.10x
Difference = 1.10x - 0.85x = 0.25x = 180
x = 180/0.25 = 720
A, B, and C can complete a task in 12, 15, and 20 days respectively. They start working together, but A leaves after 4 days. In how many more days will B and C finish the remaining work?
A's 1 day work = 1/12
B's 1 day work = 1/15
C's 1 day work = 1/20
Combined 1 day work = 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5
Work done in 4 days = 4 × 1/5 = 4/5
Remaining work = 1 - 4/5 = 1/5
B and C's combined 1 day work = 1/15 + 1/20 = 4/60 + 3/60 = 7/60
Days to finish remaining work = (1/5) / (7/60) = 12/7 ≈ 1.71 days
The average of 5 consecutive odd numbers is 41. Find the largest number.
For consecutive odd numbers, the average equals the middle number.
Middle number = 41
The 5 numbers are 37, 39, 41, 43, 45.
A vessel contains a mixture of milk and water in the ratio 4:1. 10 liters of the mixture is removed and replaced with water. If the new ratio becomes 2:3, find the initial quantity of the mixture.
Let initial quantity = x liters. Milk = (4/5)x, Water = (1/5)x
After removing 10 liters of mixture (ratio unchanged) and adding 10 liters water:
Milk left = (4/5)x - (4/5)(10) = (4/5)(x - 10)
Water left = (1/5)x - (1/5)(10) + 10 = (1/5)(x - 10) + 10
New ratio: [(4/5)(x-10)] / [(1/5)(x-10) + 10] = 2/3
Cross-multiply:
3 × (4/5)(x-10) = 2 × [(1/5)(x-10) + 10]
(12/5)(x-10) = (2/5)(x-10) + 20
(10/5)(x-10) = 20
2(x-10) = 20
x - 10 = 10
x = 20
A sum of ₹5,000 is lent at simple interest. After 3 years, the amount becomes ₹6,200. Find the rate of interest.
SI = Amount - Principal = 6200 - 5000 = ₹1,200
SI = (P × R × T)/100
1200 = (5000 × R × 3)/100
1200 = 150R
R = 8%
Pointing to a photograph, a man says, "She is the daughter of my grandfather's only son." How is the girl related to the man?
"My grandfather's only son" = the man himself (since he's the only son of his grandfather, assuming no uncles on that side).
So "She is the daughter of the man" means she is his daughter.
Find the next term: 2, 1, 1/2, 1/4, ?
Each term is half of the previous term.
2 → 1 → 1/2 → 1/4 → 1/8
A man walks 10 km towards North, then turns right and walks 6 km, then turns right again and walks 10 km. How far and in which direction is he from his starting point?
Starting point: (0, 0)
Walk 10 km North: (0, 10)
Turn right (facing East), walk 6 km: (6, 10)
Turn right (facing South), walk 10 km: (6, 0)
Distance from start = √((6-0)² + (0-0)²) = 6 km, direction East
In which year was Rahul born?
Statement 1: Rahul at present is 25 years younger than his mother.
Statement 2: Rahul's brother, who was born in 1964, is 35 years younger than his mother.
From statement 2, we know the mother's age relative to a fixed birth year (1964 + 35 = mother's birth year basis), but we don't know the current year or Rahul's exact age from statement 1 alone.
Combining both statements: the age gap between Rahul and his brother = 35 - 25 = 10 years. Since the brother was born in 1964, Rahul was born in 1964 + 10 = 1974.
Find the odd one out: Analogy pair check — "Nightly : Daily" is most similar to which pair?
Options: (a) Black : White (b) Nocturnal : Diurnal (c) Sunset : Sunrise (d) None of the above
"Nightly" relates to night-time occurrence, and "Daily" relates to day-time/every-day occurrence — this is the relationship between "occurring at night" vs "occurring during the day", which matches "Nocturnal" (of the night) and "Diurnal" (of the day).