From the following figure,

∠APO = 35°

As we know,

∠APO = ∠BPO = 35° (ΔAPO ≅ ΔBPO)

Given:

B(1995 + 1998) = 1620 + 1600

A(1996 + 1997) = 1590 + 1750

Solution:

The total number of coolers sold by shopkeeper B in 1995 and 1998 = 1620 + 1600 = 3220

The total number of coolers sold by shopkeeper A in 1996 and 1997 = 1590 + 1750 = 3340

difference = 3220 - 3340 = -120

⇒ less

Required percentage = 120/3340 x 100 = 3.5% ~ 4% less

Hence, the correct option is 2.

Squaring both sides

5x = x²

⇒ x² – 5x = 0

⇒ x × (x – 5) = 0

⇒ x = 5 and x = 0

The square root of any positive number cannot be 0.

Therefore, x = 0 will not be considered.

∴ The value of the given expression is 5.

Shortcut Trick

The value of the expression is y

∴ The value of the given expression is 5.

According to above diagram,

In ΔABC

tan45° = AB/BC

⇒ 1 = 220/BC

⇒ BC = 220 meter

In ΔABD

⇒ tan30° = AB/BD

⇒ 1/√3 = 220/BD

⇒ BD = 220√3 meter

The distance between the two points (CD) = BD - BC

⇒ The distance between the two points = 220√3 - 220

⇒ The distance between the two points = 220(1.732 - 1) = 161.05 meter

We know that, SI = Prt/100

Where, SI = simple interest, P = principal, r = rate of interest, t = number of years

Let the principal be P, and the rate be r.

Given,

SI = P/9

And t = r

Hence,

Given:

Rs. 3550 is divided into X, Y and Z

three times of X's share is equal to 5 times of Y's share and 7 times of Z's share.

Solution:

3X = 5Y

Calculation:

(x²y - xy²)+ (x - y) 

⇒ xy(x - y) + (x - y)

⇒ (x - y)(xy + 1)

∴ From the given options, (xy + 1) is one of the factors of the given expression

Given:

Divyanshu and Manish can do the work in 75/8 days

Calculation:

Let the time taken by Manish to do the work be x days

∴ (1/25) + (1/x) = 8/75

⇒ 1/x = (8/75) – (1/25)

⇒ 1/x = (8 – 3)/75 = 5/75 or 1/15

⇒ x = 15

∴ Manish can do the work in 15 days

Shubhanshu is 50% more efficient than Manish

⇒ Time taken by Shubhanshu = 15 × (100/150) = 10 days

Gurpreet takes twice the time that of Shubhanshu

⇒ Time taken by Gurpreet = 10 × 2 = 20 days

∴ Ratio of time taken by Divyanshu, Manish, Shubhanshu and Gurpreet = 25 ∶ 15 ∶ 10 ∶ 20 = 5 ∶ 3 ∶ 2 ∶ 4      ----(LCM = 60)

⇒  Ratio of there efficiencies = 12 ∶ 20 ∶ 30 ∶ 15      

∴ Wage received by Gurpreet and Shubhanshu together 

⇒ {(30 + 15)/77} × 1540 = Rs.900

∴ The wage received by Gurpreet and Shubhanshu together is Rs. 900

According to the given data,

Let X kg of rice costing ₹18 per kg be mixed with 30 kg of rice costing ₹14 per kg = (X x 18) + (30 x 14)

Resultant mixture = 15 (X + 30)

(X x 18) + (30 x 14) = 15 (X + 30)

18X + 420 = 15X + 450

18X - 15X = 450 - 420 

3X = 30 

X = 10 kg

So 10 kg of rice costing ₹18 per kg must be mixed with 30 kg of rice costing ₹14 per kg so that the resultant mixture will cost ₹15 per kg.

Alternate Method

Let's solve this using the allegation method:

1. The cost of the cheaper rice is ₹14 per kg and the cost of the dearer rice is ₹18 per kg.

2. The mean price is ₹15 per kg.

The formula for the allegation method is:

Given:

In first blend apple juice to orange juice ratio = 20% : 80 % = 1 : 4

In another blend apple juice to orange juice ratio = 70% : 30% = 7 : 3

In mixture ratio of apple juice to orange juice = 4 : 3

Calculations:

Let the ratio of the first and second blend be K : 1.

Then, according to question,

The ratio of apple juice to orange juice in the mixture

Hence, the required ratio is 9 : 26.

Shortcut Trick

Mixture (I) -

Quanity of Apple = 20% and quantity of Orange = 80%

So, Apple : orange = 20 : 80 = 1 : 4

Mixture (II) -

Quanity of Apple = 70% and quantity of Orange = 30%

So, Apple : orange = 70 : 30 = 7 : 3

In mixture ratio of apple juice to orange juice = 4 : 3

Thus, required ratio 

⇒ 9/70 : 13/35

⇒ 9 : 26

Hence, the required ratio is 9 : 26.