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Given

Rajesh is 10 years younger to Baskar, 10 years back, Rajesh's age was two thirds that of Baskar's. 

Concept used

Ratio and proportion

Calculation

Let the present age of Baskar be x years.

Rajesh's present age = x - 10

10 years back, Rajesh's age was two thirds that of Baskar's. 

⇒ \(x - 20 = \frac{2}{3}\left( {x - 10} \right)\)

⇒ 3x - 60 = 2x - 20

⇒ x = 40

Baskar is of 40 years now.

Given

Principal = Rs.1250

Amount = Rs.10000

Rate = 12.5%

Concept used

Simple interest

Calculation

Interest = Amount - Principal

Interest = 10000 - 1250

Interest = Rs.8750

Let the time be n years.

Si = \(\frac{{P\ \times\ R\ \times\ T}}{{100}}\)

\(8750 = \frac{{1250\ \times\ 12.5\ \times\ n}}{{100}}\)

n = \(\frac{{700}}{{12.5}}\)

n = 56 years.

Given

Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. 

Concept used

Time and work

Calculation

Total work = Number of days × efficiency 

A + B does a work in 6 days

B + C does a work in 10 days

C + A does a work in 7.5 days

Take Lcm of (6,10,7.5) which is 450

Total work = 450 units

Efficiency of A + B = 450/6 = 75

Efficiency of B + C = 450/10 = 45

Efficiency of A + C = 450/7.5 = 60

Total efficiency of A, B and C = (75 + 45 + 60) / 2

Total efficienct of A, B and C = 90

Number of days = 450 / 90

Number of days taken by A, B and C working together = 5 days.

Given

Nikita takes as much time in running 18 meters as a car takes in covering 48 meters.

Concept used

Time and Distance

Calculation

Time taken by Nikita = Time taken by Car

Time = Distance / Speed

⇒ \(\frac{{{d_1}}}{{{S_{nikita}}}} = \frac{{{d_2}}}{{{S_{Car}}}}\)

⇒ \(\frac{{18}}{{{S_{nikita}}}} = \frac{{48}}{{{S_{Car}}}}\)

⇒ \(\frac{{{S_{nikita}}}}{{{S_{Car}}}} = \frac{{18}}{{48}} = \frac{d}{{1600}}\)

⇒ distance = 600 m

Given

A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only.

Concept used

Time and work

Calculation

Total work = Number of days × Efficiency

Take Lcm of (16, 12 and 4) which is 48

Efficiency of A = 48/16 = 3 unit

Efficiency of B = 48/12 = 4 unit

Efficiency of A + B + C = 48/4 = 12

Efficiency of C = 12 - (3 + 4)

Efficiency of C = 12 - 7

Efficiency of C = 5 unit

C alone can do the work in 48/5 = 9 (3/5) days.

Given

Selling price is doubled, the profit triples.

Concept used

Profit and Loss

Calculation

Let the CP be x and SP be y

As per the question,

⇒ 2y - x = 3(y - x)

⇒ 2y - x = 3y - 3x

⇒ 2x = y

⇒ \(\frac{x}{y} = \frac{1}{2}\)

CP = 1 unit, SP = 2 unit

Gain = 1 unit

Profit % = \(\frac{1}{1} \times 100 \)

Profit % = 100%

According to the given information :

1. A and P are at the ends. R is sitting to the left of A (Thus, A will be to the extreme right).
2. S and Z are in the centre (Two cases are possible).
3. The vacant place will be occupied by X.

Thus, it is clear from both the cases that X is to the right of P.

Hence, the correct answer is "X".

Given

Two numbers are respectively 20% and 50% more than a third number.

Concept used

Ratio and proportion

Calculation

Let the third number be 100

Let the first and second numbers be A and B

A is 20% more than 100 = 120

B is 50% more than 100 = 150

A : B = 120 : 150

A : B = 12 : 15

A : B = 4 : 5

Given

Salaries of ravi and Sumit are in the ratio 2 : 3.

If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. 

Concept used

Ratio and proportion

Calculation:

Let the initial salaries of Ravi and sumit be 2x and 3x

As per the question,

⇒ \(\frac{{2x\ +\ 4000}}{{3x\ +\ 4000}} = \frac{{40}}{{57}}\)

⇒ 57(2x + 4000) = 40(3x + 4000)

⇒ 6x = 68000

⇒ 3x = 34000

Sumit's present salary = 3x + 4000

⇒ Rs.(34000 + 4000) = Rs.38000

∴ Sumit's present salary is Rs. 38000

Alternate Method Given:

Salaries of ravi and Sumit are in the ratio 2 : 3.

If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57

Calculation:

To balance the given ratio, we need to multiply (before)Salary with 17 .

6 = 4000

1 = 4000/6

57(incremented salary) = (4000/6) × 57

⇒ 38,000

∴ Sumit's present salary is Rs. 38000

Given

P and Q can finish a work in 15 & 10 days. Q starts the work and leaves it after 5 days. 

Concept used

Time and work

Calculation

Total work = Number of days × Efficiency

Lcm of (15 and 10) is 30 

Total work = 30 units

Efficiency of P = 30/15 = 2 unit

Efficiency of Q = 30/10 = 3 unit

Q does the work for 5 days = 5 × 3 = 15 work done

Remaining work = 30 - 15 = 15 unit

P does the work = (Remaining work) / efficiency

P does the work in = 15/2 days.