Research Aptitude Test - 1

1. Let the distance between the two starting points be D.
   Let S ₁and S ₂be the speeds of the two cars, respectively.

2. They meet in 3 hours 20 minutes, which is 3 + 20/60 = 3.333 …hours = 10/3 hours.
   Since they travel towards each other, (S ₁+ S ₂)(10/3) = D.
   So, S ₁+ S ₂= 3D/10.

3. The first car arrives at the second car ’s starting point 5 hours later than the second car arrives at the first car ’s starting point.
   In other words, the difference between their total travel times for the whole distance is 5 hours.

4. Let T ₁be the time the first car needs to travel the entire distance (D / S ₁), and T ₂be the time the second car needs (D / S ₂).
   From step 3, assume T ₁= T ₂+ 5. (This means the first car takes longer, so it ’s the slower car.)

5. From S ₁+ S ₂= 3D/10 and S ₁= D/T ₁, S ₂= D/T ₂, we get:
   D(1/T ₁+ 1/T ₂) = 3D/10
   ⇒1/T ₁+ 1/T ₂= 3/10.

6. Substitute T ₁= T ₂+ 5 into 1/T ₁+ 1/T ₂= 3/10, solve for T ₂:
   You ’ll get T ₂= 5 hours, and then T ₁= 10 hours.

Time take for reaching B for ram is T = 5/5 = 1hr
Time taken for reaching B for Shyam is T = 5/10 = 1/2 hr

Its 10 am when ram reaches B and 10: 15 when Shyam reaches B , so they must meet each after 10 and before 10:15 for sure as ram starts back after reaching B

if we see for options 10: 10 am is the only answer

To solve the problem of determining the speed of the second rabbit, follow these steps:

• The second rabbit covers 7/120 of the distance in 2 hours 30 minutes .
• This translates to 7% of the distance in that time span.
• To find the equivalent time for 3 hours , calculate the distance covered as 8.4/120 , which is 7% of the total distance.
• In 3 hours , both rabbits together cover 15% of the total distance:
  • First rabbit covers 8% .
  • Second rabbit covers 7% .
• Thus, they cover 15% per 3 hours , meeting in 20 hours as they jointly cover all of the distance.
• The ratio of their speeds is 8:7 . Given the first rabbit travels 800 feet to meet:
  • Therefore, the second rabbit covers 700 feet to the meeting point in 20 hours .
• The speed of the second rabbit is calculated as 700 feet / 20 hours = 35 feet/h .

Therefore, the correct answer is 35 feet/h .

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x)

⇒28x - 22x = 350800 - (13900 * 22)
⇒6x = 45000
⇒x = 7500
So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400

Let the number of total employees in the company be 100x, and the total salary of all the employees be 100y.

It is given that  20% of the employees work in the manufacturing department, and  the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company.

Hence, the total number of employees in the manufacturing department is 20x, and the total salary received by them is (100y/6)

Average salary in the manufacturing department = (100y/6*20x) = 5y/6x

Similarly, the total number of employees in the nonmanufacturing department is 80x, and the total salary received by them is (500y/6)

Hence, the average salary in the nonmanufacturing department = (500y/6*80x) = 25y/24x

Hence, the ratio is:- (5y/6x): (25y/24x) 

=>120: 150 = 4:5

The correct option is D

1st term = 2
2nd term = 2 + 1 = 3
3rd term = 3  * 1 = 3
4th term = 3 + 2 = 5
5th term = 5  * 2 = 10
6th term = 10  + 3  = 13...

⇒For every term at even position, previous term is added with half of the position
⇒For every term at odd position, previous term is multipiled with the same numeber that was added in previous term

So, missing term = 13 x 3 = 39.

Shortcut:
The decrease in weight would be 20kgs (10people ’s average weight drops by 2 kgs). Hence, the new person ’s weight = 140 - 20 = 120.

Detailed Solution:

Let weight of 9  men =x.
Weight of new men =y

According to the question:

((x+140)/10) ​−2 = (x+y ​)/10
y = 120

P - M  → P is the brother of M
M + N  → M is the mother of N
N  × Q  → N is the sister of Q
Therefore, P is the maternal uncle of Q.

option D.

P*Q^R@S#T*P: P is elder than Q, Q is child of R, R is brother of S, S is younger than T, T is elder than  P.
The age of Q is 22 years and age of T is 33 years.

T(33) >P >Q
Hence, the age of P is 29 years.

Explanation:

Given Information:
- P!Q - P is the parent of Q
- P^Q - P is the child of Q
- P*Q - P is elder to Q
- P#Q - P is younger to Q
- P@Q - P is brother of Q
- P &Q - P is wife of Q
- P+Q - P is sister-in-law of Q

Given:
A!B^C+D &E@F^GIA

Since G is the wife of H, we can infer that G &H.

Now, we need to find the relationship between G and C.

Since H is the parent of G, and C is the child of B, and B is the parent of C, then we can conclude that G is the mother-in-law of C.

Therefore, the correct answer is B: Mother-in-law .A ! B ∧C + D &E @ F ^ G! A: A is parent of B, B is child of C, C is sister-in-law of D, D is wife of E, E  is brother of F, F is child of G, G is parent of A.