Given:

A shopkeeper gives a 35% discount on the marked price of a bottle with a selling price of ₹1,755.

Formula used:

∴ The marked price of the bottle is Rs. 2700.

Given:

Monthly income is Rs. 13500 and monthly expenses is Rs. 9000,

In the next year the monthly income increased by 14% and the expenses increased by 7%.

Formula used:

Income = expenditure + savings

Calculations:

When income is Rs. 13500 and expenditure is Rs. 9000, the savings = 13500 - 9000 = Rs. 4500

In the next year, income increases by 14%, 13500 + 13500 × 14%

∴ The answer is 28%

Calculation:

As per the question,

 sin P + sin Q + sin R = QR/PR + 1 + PQ/PR

The sine of a 90-degree angle is always 1, because for a right angle, the opposite side and the hypotenuse are equal.

= 4/5 + 1 + 3/5

= 12/5

Substituting the values of trigonometric functions-

Given:

OA = 450 units

OB = 300 units

Calculation:

Angle of elevation from point B is equal to the angle of depression from top to point B.

Angle of elevation from point B = 60°

Now in ΔPOB, for ∠PBO = 60°

⇒ tan60° = OP/OB

⇒ OP = 300 × √3 = 300√3 units

Now in ΔMOA,

⇒ tan30° = OM/OA

⇒ OM = (1/√3) × 450 = 150√3 units

Required height = MP = OP – OM

⇒ Required height = 300√3 - 150√3

⇒ Required height = 150√3 units

Given:

AB || CD, ∠ABE = 110°, ∠ECD = 95°

Concept:

Properties of lines and angles.

Calculation:

Let AB is parallel to FG, then ∠ABE = ∠BEG = 110° (Alternate angles)

Also, it is given that CD is parallel to AB and we have assumed that AB is parallel to FG, then CD is parallel to FG .

Therefore, considering CD║FG and CE is the transversal,

Then ∠DCE + ∠CEG = 180° (Co-interior angles)

95° + ∠CEG = 180°

∠CEG = 85°

Now, ∠BEG = ∠BEC + ∠CEG

110° = x + 85°

x = 25°

Thus, the value of the ∠BEC = x = 25°.

The correct answer is '25º'.

Calculation:

Total discount on all the articles = 600 + 300 + 600 + 500 + 400 + 300 + 300 = 3000

Total marked price of all the articles = 1200 + 800 + 1000 + 700 + 500 + 600 + 1100 = 5900

Percentage of total discount to total marked price = 3000/5900 × 100 = 50.84%

∴ Option 2 is the correct answer.

Given:

The ratio of the present age Chinky and Minky = 4 ∶ 5

The present age of Chinky’s mother = (9/2) × Minky’s age 5 years ago

The present age of Minky’s mother = (7/3) × Chinky’s age after 3 year

Concept used:

Divide the age according to ratio.

Formulae used:

Average Age = Sum of total age/Total person

Calculations:

Let the present age of Chinky be 4x and Minky be 5x

5 year ago Minky’s age = 5x – 5

The present age of Chinky’s mother = (9/2) × Minky’s age 5 years ago

So, the present age of Chinky’s mother = (9/2) × (5x – 5)

⇒ (45x – 45)/2

After 15 years, Chinky’s mother age = ((45x – 45)/2) + 15

⇒ (45x – 15)/2

Chinky’s age after 3 years = 4x + 3

The present age of Minky’s mother = (7/3) × Chinky’s age after 3 year

So, the present age of Minky’s mother = (7/3) × (4x + 3)

⇒ (28x/3) + 7

After 15 years, Minky’s mother age = (28x/3) + 7 + 15

⇒ (28x + 66)/3

Total age of Chinky’s mother and Minky’s mother after 15 years = ((45x – 15)/2) + ((28x + 66)/3)

⇒ (135x – 45 + 56x + 132)/6

⇒ (191x + 87)/6

Average age of Chinky’s mother and Minky’s mother after 15 years = Sum of total age/Total person

⇒ (191x + 43)/(6 × 2)

⇒ (191x + 87)/12 = 55

⇒ 191x = 573

⇒ x = 3

The present age of Chinky = 4x = 4 × 3 = 12

The present age of Minky = 5x = 5 × 3 =15

The Difference between Chinky’s and Minky’s present age = 15 – 12 = 3 years

The Difference between Chinky’s and Minky’s present age is 3 years

Given:

Length of train P and Q are 270m and 330m

Solution:

According to the problem, 

Speed of Q - Speed of P = 108kmph..............1

The Sum of the speed of train P and Q = 2 x 108 = 216kmph

Speed of train P + Speed of train Q  = 216kmph............................2

From 1 & 2

Speed of train Q = 162 kmph

Speed of train P = 54 kmph

As Trains are in same direction, so relative speed = 162 - 54 = 108 kmph

Train Q crosses train P running in the same direction in 'a + 5' seconds

600/(a+5) = 108 x 5/18     (1kmph = 5/18 mps)

600/(a+5) = 30

a = 15

Length of platform that train P crosses in 'a + 35' seconds = (270 + X)/(a+35) = 54 x 5/18

(270 + X)/(15 + 35) = 15

(270 + X) = 750

X = 750 - 270 = 480m

Hence option (4) is correct.

Mistake Points

Please note that the difference between speeds of P and speed of Q means

Speed of P ~ speed of Q 

which means 

either (speed of P - speed of Q) or (speed of Q - speed of P) is true.

So we have to determine out of these two which condition is possible. Here train Q is crossing train P, this means speed of train Q is more. so the second condition is true.

So Q = 162 km/hr and P = 54 km/hr

Given:

Marks obtained in English : Hindi = 15 : 16

Marks obtained in Maths : Science = 5 : 6

Average marks obtained = 64%

Marks obtained in English = Marks obtained in Maths 

Maximum marks in each subject = 100

Formula used:

Average marks = Total marks obtained in all the subjects/Total number of subjects

Calculation:

Let the marks obtained by Yash in English and Hindi be 15x and 16x respectively.

And, the marks obtained by Yash in Maths and Science be 5y and 6y respectively.

ATQ, 15x = 5y

⇒ y = 3x

Total marks in all subject = 4 × 100 = 400

The aggregate marks obtained in the four subjects together = 64%

Therefore, (15x + 16x + 5y + 6y)  = 400 × 64%

⇒ 31x + 11y = 400 × 64/100

⇒ 31x + 11y = 256

⇒ 31x + 33x = 256 (11y = 11 × 3x = 33x)

⇒ x = 4 

⇒ y = 3x = 12

Total marks obtained in Hindi and Science together = 16x + 6y = 64 + 72 = 136

Hence, the correct answer is 136.