Arithmetic Reasoning
When Rahul was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If
Rahul's brother is 6 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he was
Explanation: Let Rahul's age be R.
His brother is 6 years older, so his brother's age = R + 6.
His father was 32 years older than his brother, so his father's age = (R + 6) + 32 = R + 38.
His mother was 3 years younger than his father, so his mother’s age = (R + 38) - 3 = R + 35.
His mother was 25 years older than his sister, so his sister’s age = (R + 35) - 25 = R + 10.
When Rahul was born (R = 0), his sister’s age = 10 years.
A man has a certain number of small boxes to pack into parcels. If he packs 3, 4, 5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcel, none is left over. What is the number of boxes, he may have to pack?
Explanation: Find the LCM of 3, 4, 5, and 6, which is 60.
Express the number in the form 60x+1, since it must leave a remainder of 1 when divided by 3, 4, 5, and 6.
Find the smallest x for which 60x+1 is a multiple of 7.
For x=5, we get 301, which satisfies all conditions.
Today is Varun's birthday. One year from today he will be twice as old as he was 12 years ago. How old is Varun today?
Explanation: Varun's age = x
One year later = x + 1
Twelve years ago = x - 12
Given: x+1=2(x−12)
Solving:
x+1 = 2x−24
25 = x
Varun is 25 years old.
In a class, 20% of the members own only two cars each, 40% of the remaining own three cars each and the remaining members own only one car each. Which of the following statements is definitely true from the given statements?
Explanation: Let total members = 100
20 own 2 cars.
40% of remaining (80) own 3 cars → 32 members.
Remaining (100 - 20 - 32) = 48 own 1 car.
A student got twice as many sums wrong as he got right. If he attempted 48 sums in all, how many did he solve correctly?