The series follows the following pattern:

24 × 1 + 1 = 25

25 × 2 + 1 = 51

51 × 3 + 1 = 154

154 × 4 + 1 = 617

617 × 5 + 1 = 3086

The series follows the following pattern:

The series follows the following pattern:

7 × 4 = 28

28 × 3.5 = 98

98 × 3 = 294

294 × 2.5 = 735

735 × 2 = 1470

The series follows the following pattern:

42 × 1 + 1 = 43

43 × 2 – 2 = 84

84 × 3 + 3 = 255

255 × 4 - 4 = 1016

1016 × 5 + 5 = 5085

The series follows the following pattern:

73 – 72 = 294

83 – 82 = 448

93 – 92 = 648

10³ – 10² = 900

11³ – 11² = 1210

12³ – 12² = 1584

GIVEN :

A man is thrice as fast as a women 

A woman is twice as fast as a boy

All of them can do a work in 18 days

CONCEPT :

Total work = Total efficiency × Total time

CALCULATION :

Let the efficiency of the boy is x

As per the question,

The efficiency of woman = 2x

The efficiency of man = 6x

The ratio of their efficiency (Man ∶ Woman ∶ Boy ) = 6x ∶ 2x ∶ x

The total efficiency of Man, Woman and Boy = 6x + 2x + x = 9x 

Total work done by all Man, Woman and Boy = 9x × 18 = 162x

Number of days taken by a boy = 162x/x = 162

∴ The number of days taken by a boy is 162.

GIVEN :

The ratio of ages of mother and daughter 7 years ago was 6 : 1

The ratio of ages of mother and daughter after 3 years will be 8 : 3

The ratio of present age of father and daughter is 10 : 3

ASSUMPTION :

Let the age of mother and daughter 7 years ago was 6x and x

So, the age of mother and daughter after 3 years will be (6x + 10) and (x + 10)

CALCULATION :

According to question,

∴ Present age of father is 40 years

Given:

The ratio of income of A to that of B is 7 : 9

They together save Rs. 10000 and their savings are in the ratio 2 : 3

And the expenditure of B is 25% more than that of A

Calculation:

Let the income of A and B be 7x and 9x

And let their savings are in the ratio 2y and 3y

According to question,

2y + 3y = 10000

⇒ 5y = 10000

So, y = 2000

So, savings of A and B are Rs. 4000 and Rs. 6000

So, the expenditure of A = Rs. (7x – 4000)

And the expenditure of B = Rs. (9x – 6000)

Now, again according to question

(9x – 6000) = 125% of (7x – 4000)

⇒ (9x – 6000) = 5/4 × (7x – 4000)

⇒ 4 (9x – 6000) = 5 (7x – 4000)

⇒ 36x – 24000 = 35x – 20000

So, x = 4000

∴ The total income of A and B = 16x = 16 × 4000 = Rs 64000.

Given:

A dishonest seller at the time of selling uses weight 22% less.

A dishonest seller at the time of purchasing uses weight 30% more.

Formula Used:

Profit% = (Selling price - Cost price)/Cost price × 100

Calculation:

C.P of 1300 gm = Rs. 1000

CP of 780 gm = Rs. 600

SP of 780 gm = Rs. 1000

Required profit percentage = (400/600) × 100 = 66.66% approx.

∴ The profit% earned by him is 66.66%.

Alternate Method:

Let the original weight be 1000 gm.

The shopkeeper buys by cheating = 1300 gm

The shopkeeper sell by cheating = 1000 × (100 - 22)/100 = 780 gm

Total cheat weight = 1300 - 780 = 520 gm

The profit% = Cheat weight/actual weight given × 100

The profit% = 520/780 × 100 = 66.66%

∴ The profit% earned by him is 66.66%.

Let the number of Levis jeans ordered = x 

Price of each Blackberry jeans = Rs a per unit

Then, price of each Levis jeans = Rs 2a per unit

According to the question,

(6a + 2a x) = (2a × 6 + a x) × 140/100

⇒ 30 a + 10 a x = 84 a + 7 a x

Therefore, x = 18

∴ Required ratio = 6 : 18 = 1 : 3