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Given:

Investment amount ratio of A and B = 3 : 5

Profit of A is Rs.3450

Calculation:

Current Ratio = 3 : 5

Ratio of Next year = 3 × 110% : 5 × 88% = 3 : 4

A's Profit = Rs. 3450

Total Profit = 3450 × (7/3) = Rs.8050

∴ The total profit is Rs. 8050.

Given:

Amount invested on simple interest = Rs. 11000

Formula:

Let P = principal, R = rate of interest and N = time period

Simple Interest (S.I.) = PNR / 100

Compound interest (C.I.) = P(1 + R / 100)ⁿ – P

Calculation:

S.I. earned by Raj in two years = 11000 × 2 × 20 / 100 = Rs. 4400

Total amount invested on C.I. after 2years = 11000 + 4400 = Rs. 15400

C.I. in 2 years = 15400(1 + 20 / 100)² – 15400 = Rs. 6776

Total amount he got after 4 years = 15400 + 6776 = Rs. 22176

Total profit = 22176 – 11000 = Rs. 11176

Given:

Downstream speed = 10 km/hours more than Upstream speed

Speed of Boat in still water = 9 km/hr

Upstream Distance = 48 km

Downstream Distance = 56 km

Formula used:

Time taken = Distance/Speed

Downstream speed = Speed of Boat in still water + Speed of Stream

Upstream speed = Speed of Boat in still water – Speed of Stream

Calculation:

Let speed of stream be y km/hr

Speed of boat in still water = 9 km/hr

Downstream speed = (9 + y) km/hr

Upstream speed = (9 – y) km/hr

Downstream speed = 10 + Upstream speed

⇒ 9 + y = 10 + 9 – y

⇒ 2y = 10

⇒ y = 5 km/hr

Now, Downstream speed = (9 + 5) = 14 km/hr

⇒ Upstream speed = (9 – 5) = 4 km/hr

Time to cover 56 km Downstream = 56/14 hour

⇒ Time taken = 4 hours

Time to cover 48 km Upstream = 48/4 hour

⇒ Time taken = 12 hours

Total time taken = (4 + 12) hours

⇒ 16 hours

∴ The total time taken is 16 hours.

Given:

The number of marbles with A and B together = 50% of that with C

The difference between the no. of marbles with B and C = 37

The no. of marbles with A =12, 

Calculation:

Let A, B and C be the number of marbles be  A, B and C respectively.

Given A + B = (1 / 2) × C

⇒ 2(A + B) = C

⇒ 2A + 2B = C

⇒ 2(12) + 2B = C

⇒ 24 + 2B = C

⇒ C - 2B = 24     ---(1)

⇒ C - B = 37     ---(2) C > B as it is given A + B = 1 / 2 × C

Multiplying (2) with 2

2C - 2B = 74     ---(3)

Subtracting equation 1 from equation 3

∴ We get C = 50

 

Given:

The number of marbles with A and B together = 50% of that with C

The difference between the no. of marbles with B and C = 37

The no. of marbles with A =12, 

Calculation:

Let A, B and C be the number of marbles be  x, y and z respectively.

According to the question,

x + y = z × 50/100 = z/2

⇒ x + y = z/2     ----(1)

z - y = 37     ----(2), z > y as it is given x + y = 1 / 2 × z

From equation(1);

x + y = z/2 

⇒ 12 + y = z/2

⇒ y - z/2 = -12

⇒ (2y - z)/2 = -12

⇒ z - 2y = 24     ----(3)

Subtract from eq(1) to eq(2):

z - y - z + 2y = 37 - 24

⇒ y = 13

Putting the value of y = 7, in eq(3);

z - 2y = 24

⇒ z - 2 × 13 = 24

⇒ z - 26 = 24 

⇒ z = 24 + 26 = 50

∴ The no. of marbles with C is 50.

Speed of the train = (90 × 5/18) = 25 m/s

Let the length of train be y.

Let the length of platform be x.

Length of the bridge = 2x

Distance covered by the train to pass the platform = 25 × 30 = 750 m

(x + y) = 750     ---- (i)

Distance covered by the train to pass the bridge = 25 × 36 = 900 m

(2x + y) = 900    ---- (ii)

From (i) and (ii),

 y = 600 m and x = 150 m

∴ Length of the train = 600 m

1)K is sitting second to the left of L. 

2)P is sitting to the immediate left of M

3)Three-person are sitting between K and N.Hence, Case 3 not follows

4) R is not an immediate neighbor of L

5)N is not an immediate neighbour of Neither P nor O.Hence, Case 2 not follows

The final arrangement will be

Hence, the position of O with respect to P in an anticlockwise direction is Third to the right of P.

1)K is sitting second to the left of L. 

2)P is sitting to the immediate left of M

3)Three-person are sitting between K and N.Hence, Case 3 not follows

4) R is not an immediate neighbor of L

5)N is not an immediate neighbor of Neither P nor O.Hence, Case 2 not follows

The final arrangement will be

Hence, O is the immediate right of K.

1)K is sitting second to the left of L. 

2)P is sitting to the immediate left of M

3)Three-person are sitting between K and N.Hence, Case 3 not follows

4) R is not an immediate neighbor of L

5)N is not an immediate neighbor of Neither P nor O. Hence, Case 2 not follows

The final arrangement will be

Hence, L is sitting opposite P.

1)K is sitting second to the left of L. 

2)P is sitting to the immediate left of M

3)Three-person are sitting between K and N.Hence, Case 3 not follows

4) R is not an immediate neighbor of L

5)N is not an immediate neighbour of Neither P nor O.Hence, Case 2 not follows

The final arrangement will be

Hence, from the above figure, we say that three-person are sitting between N and K.

1)K is sitting second to the left of L. 

2)P is sitting to the immediate left of M

3)Three-person are sitting between K and N.Hence, Case 3 not follows

4) R is not an immediate neighbor of L

5)N is not an immediate neighbour of Neither P nor O.Hence, Case 2 not follows

The final arrangement will be

Hence, from the above figure, we say that 2 people are sitting between the immediate left of K and N.