Given:

Today, the age of a father is thrice the age of his son.

After 5 years, the age of father will be 2.5 times the age of his son.

Calculation:

Let, the age of the father = f

age of the son = s

⇒ f = 3s    → (1)

⇒ (f + 5) = 2.5(s + 5)   → (2)   

On putting the value of f from eq(1) in eq(2),

⇒ 3s + 5 = 2.5s + 12.5

⇒ 0.5s = 7.5

⇒ s = 15

∴ The age of son today is 15 years.

Let cost price per cm = Rs 1,

Hence, cost price of 90cm = Rs 90

And, cost price of 100cm = Rs 100

Selling price of 100cm = 100 + 10% = Rs 110

∴ Actual profit percent = {(110 – 90)/90} × 100%

= (2/9) × 100% = 22.22%

Hence, the actual profit percent gained by the shopkeeper is 22.22%.

Given:

Investment time of Anil = 9 months

Investment time of Sunil = 12 months

Annual profit = Rs. 28,000

Concept used:

Calculation:

Let the initial investment of Sunil and Anil = Rs. x

Amount invested by Sunil = 12x

Amount invested by Anil = 9x

12x + 9x = 28000  

21x = 28000

= Rs. 16,000

Thus  , the correct answer is Rs. 16,000.

Given:

Ratio of two numbers = 3:8

Sum of the numbers = 88

Concept:

The sum of numbers in the ratio

Solution:

⇒ Let the two numbers be 3x and 8x

⇒ 3x + 8x = 88

⇒ x = 8

Therefore, the smaller number is 3x = 3 × 8 = 24.

Concept Used:

Follow the BODMAS rule according to the table given below:

⇒ 84

∴ The value 5 × [6 × 2{3 × 7 ÷ (5 × 3)} is 84.

Given:

Length of the train = L m

Length of the first Bridge = 340 m

Time taken to cross first Bridge = 35 seconds

Length of the Second Bridge = 460 m

Time taken to cross second Bridge = 38 seconds

Concept:

When a train crosses a bridge, it travels a distance equal to its own length and the length of the bridge.

Common mistake:

These types of questions, the conversion of speed in meter/seconds into Km/hr should be done carefully.

Unit conversion from Km/hr to m/s, then multiply from 5/18.

Unit conversion from m/s to Km/hr, then multiply from 18/5.

FORMULA USED:

Speed = (Distance)/(Time)

CALCULATION :

The train crosses First bridge in 35 sec,

∵ Length of train + Length of First bridge = L + 340

⇒ Speed of train = (L + 340)/(35)

The train crosses Second bridge in 38 sec,

∵ Length of train + Length of Second bridge = L + 460

⇒ Speed of train = (L + 460)/(38)

According to Question,

Speed of train will be same

(L + 340)/(35) = (L + 460)/(38)

On solving we get,

⇒ Length of train, L = 1060 m

⇒ Speed of train = (1060 + 340)/(35)

⇒ Speed of train = (1400)/(35) = 40 m/s

⇒ Speed of train = 40 × 18/5 = 144 Km/hr

Given:

Time to go 120 km upstream and come back to the starting point = 8 hours

The speed of the stream is 25% of the speed of the boat in still water

Formula Used:

Downstream Speed = Speed of boat + Speed of stream 

Upstream Speed = Speed of boat - Speed of stream

Calculation:

Let the speed of the boat in still water be x km/h.

So, the speed of stream = x × 25/100 = (x/4) km/h

The upstream speed of boat = x – (x/4) = (3x/4) km/h

The downstream speed of boat = x + (x/4) = (5x/4) km/h

According to the question:

[120/ (3x/4)] + [120/ (5x/4)] = 8

⇒ (480/3x) + (480/5x) = 8

⇒ 480[(5 + 3) /15x] = 8

⇒ 15x = 480

⇒ x = 32

⇒ The upstream speed of the boat = 32 × 3/4 = 24 km/h

⇒ The downstream speed of the boat = 32 × 5/4 = 40 km/h

∴ The required difference = 40 – 24 = 16 km/h

Shortcut Trick

Ratio of days = 6 : 4 : 9

Ratio of daily wages =  5 : 6 : 4

Ratio of total wages = 30 : 24 : 36 = 5 : 4 : 6

15 units = 1800

5 units = 1800/15 × 5 = Rs. 600

Calculation:

Ratio of wages of A, B and C = 5 : 6 : 4

Number of days for which A worked = 6 days

⇒ A’s share = 6 × 5 = 30

Number of days for which B worked = 4 days

⇒ B’s share = 4 × 6 = 24

Number of days for which C worked = 9 days

⇒ C’s share = 9 × 4 = 36

A’s share : B’s share : C’s share = 30 : 24 : 36 = 5 : 4 : 6

⇒ A’s share = 5/(5 + 6 + 4) × 1800 = 5/15 × 1800 = Rs. 600

∴ A’s share is Rs. 600

Given:-

Time for A = 60 minutes

Time for B = 90 minutes

Time for A, B, and C = 45 minutes

Concept:-

Basic time and work concept.

Capacity = time × efficiency

Calculation:-

Let the time for C be x.

1/60 + 1/90 + 1/c = 1/45

1/x = 4/180 – 5/180

x = -180

Here -ve sign shows that C is the drain pipe.

Time ratio of A and C = 60 : 180

Efficiency is inversely proportional to the time

∴ Efficiency ratio = 180:60 = 3 : 1