Q. 1: If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2:1, then which one of the following is a possible value of (a + b + c)?
,Correct Answer:- C
Explanation:- a : b = 3 : 4 and b : c = 2 : 1 Multiplying the second ratio by 2, we have
a : b = 3 : 4 b : c = 4 : 2
Therefore, a : b : c = 3 : 4 : 2.
⇒ a = 3k, b = 4k, c = 2k.
Since a, b and c are positive integers, their sum should be 9k, a positive integer. From the options, only choice (3), which is 207, is a multiple of 9.
Correct Answer:- B
Explanation:- The motorbike that left A travelled 168 km from 1:00 p.m. to 3:40 p.m., i.e. in 2 2/3 hours or 8/3 hours. The car that left B, started at 2:00 p.m. and travelled till 3:40 p.m., i.e. for 1 2/3 hours or 5/3 hours.
The car would’ve travelled 5/8th of the distance as the bike, but since the car travelled at twice the speed, the car would’ve travelled 10/8th of the distance, i.e. (10/8) x 168 = 210 km.
Therefore, total distance between A and B = 168 + 210 = 378 km.
Q. 3: Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamal’s share, in rupees, is
Correct Answer:- A
Explanation:- The team completes the job in 4 days.
Since Amol needs 10 days to complete the job, in 4 days, he does 4/10th or 40% of the work. Since Bimal needs 8 days to complete the job, in 4 days, he does 4/8th or 50% of the work.
Therefore, Kamal did 10% of the work and for doing 10% of the work, he gets 10% of the payment, i.e. Rs. 100.
Q. 4: Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4:3:2. Then the resulting mixture has
A) The same amount of water and liquid B
B) The same amount of liquids B and C
C) More water than liquid B
D) More water than liquid A
Correct Answer:- C
Explanation:- First mixture has 2/3rds A and the rest water. Second mixture has 3/4ths B and the rest water. Third mixture has 4/5ths C and the rest water.
The 3 mixtures are mixed in the ratio 4 : 3 : 2. Let’s say we get a 1 litre mixture containing the three mixtures.
Q. 5: Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is
Correct Answer:- B
In ∆ABC, AB = 1 cm, BC = 1 cm As ∠B = 120,
AC2 = 12 + 12 – 2(1) (1) cos (120°) (Cosine rule)
= 12 + 12 + 1 = 3
⇒ AC = √3 cm
The square of side √3 cm will have an area of (√3 )2 = 3 cm2