The correct answer is option 4 i.e. 60 minutes

⇒ Speed of Prashant = 6/(45/60)

⇒ 8 km/h

Speed of Vedant = (3/4) × 8 = 6km/h

⇒ Time taken by Vedant = 6/6 = 1hour or 60 minutes

The correct answer is option 3 i.e. 50 years.

Here, Simple Interest = Final amount – Principal amount

Simple Interest = 23286 - 3881 = 19,405

Where, SI = Simple interest = Rs. 19,405

P = Principal amount = Rs 3881

R = Rate of interest = 10%

T = time period in years

⇒ T =19405 × 100/(3881 × 10) = 50 years

The correct answer is option 4 i.e. 26 sec.

Speed of train = 54 km/hr = 54 × 5/18 = 15 m/sec.

So, length of train = 15 × 8 = 120

So, [120 + L + 240]/15 = 30

Or, L = (15 × 30) - 120 - 240 = 90

So, required time = (120 + (90 × 3))/15 = 26 sec.

The correct answer is Option 2 i.e. 30.

let the number be A.

According to the question

∴ 20/100 × A + 120 = 60/100 A

⇒ 40/100 A = 120

⇒ A = 300

Now  30/100 × 300 - 20/100 × 300 = 30

The correct answer is Option 1 i.e. 1 hour

Concept:- Let us assume that a person changes his speed to m/n of its usual speed such that m/n < 1 and reaches his destination late by t minutes then the usual time taken by him is

T = t/(n/m - 1)

Now, according to the question,

Usual time taken by Alex = 30/(3/2 - 1)

30/(3 - 2)/2

30/1/2 = 60 minutes or 1 hour

The correct answer is option 4 i.e. 85 years.

Average = The sum of the total age/number of members

The sum of the age of 50 members = 50 × 58 = 2900

The sum of the age of members after leaving one member = 2900 - 60 = 2840

If  a new member joins the new average becomes

= 58 + 0.5 = 58.5 years

Let the age of new member = x years

2840 + x = 58.5 × 50 = 2925

x = 2925 - 2840 = 85 years

The correct answer is Option 1 i.e. 125.

If we add or multiply the same number to every terms of the group, then the average also increases and decreases according to that same proportion.

45 + 5 = 50

50 × 2.5 = 125

The correct answer is Option 3 i.e. Rs. 24827.6.

Amount invested by A = Rs. 15000

Amount invested by B = Rs 20000

Amount invested by C = Rs 16000

Total profit after 2 years = Rs. 90000

Total amount = amount invested × number of
months

Total amount invested by A = 15000(24) = Rs. 360000

Total amount invested by B = 20000(24) = Rs. 480000

Total amount invested by C = 16000(20) = Rs. 320000

The ratio of their investment = A : B : C = 360000 : 480000 : 320000 

The ratio of their investment ie. A : B : C = 9 : 12 : 8

C's share in profit = (8/29) × 90000 = 720000/29 = Rs. 24827.6

The correct answer is option 3 i.e. Rs. 7400.

We know the difference between simple and compound interest for 2 years at a similar rate = PR²/100²,

where P = Principal

R = Rate

Thus,

⇒ P × 10²/100² = Rs. 74

⇒ P = Rs. 7400

The correct answer is Option 3 i.e. 28%.

Let the Income = Rs. 13,500

Expenditure = Rs. 9000

Expenditure % = (9000/13500) × 100 = (200/3)%

We required a percentage change in savings, so

Let income = Rs. 300

Expenditure = Rs. 200

Savings = Rs. 100

Increased income = Rs. 342

Increased Expenditure = Rs. 214

New Saving = Rs. 128

Percentage of increased savings = (128 – 100) × 100/100 = 28%