**Answer and Explanation:**

1. Answer : (1) 1.4

Explanation:

Let 0.9 = x, 0.2 = y and 0.3 = z

Then, the given expression

= x * x * x + y * y * y + z * z * z – 3* x * y * z / x * x + y * y + z * z – x * y – y * z – z * x

= x^3 + y^3 + z^3 – 3xyz / x^2 + y^2 + z^2 – xy -yz – zx

= (x + y + z) (x^2 + y^2 + z^2 – xy – yz – zx) / x^2 + y^2 + z^2 – xy – yz – zx

= x + y + z

= 0.9 + 0.2 + 0.3 = 1.4

2. Answer : (2) 9cm

Explanation :

Let the length of the smaller line segment = x cm.

Therefore The length of larger line segment = (x + 2) cm.

According to the question,

(x + 2)^2 – x^2 = 32

= x^2 + 4x + 4 – x^2 = 32

= 4x = 32 – 4 = 28

= x = 28/4 = 7

Therefore The required length = x + 2 = 7 + 2 = 9cm.

3. Answer : (3) 11/13, 7/9, 3/5

Explanation :

The decimal equivalent of

3/5 = 0.6, 7/9 = 0.777……..

11/13 = 0.846

Obviously 0.846 > 0.7 > 0.6

Therefore The required decreasing order

= 11/13, 7/9, 3/5

4. Answer : (1) 4kmph

Explanation :

Let the speed of the current be x kmph.

According to the question.

6 / 6- x = 3

= 18 – 3x = 6

= 3x = 18 – 6

= x = 12/3 = 4 kmph.

5. Answer : (3) 36kmph

Explanation:

Let the speeed of each train be x kmph.

Their relative speed

= x + x = 2x kmph.

Time taken

= Total length of trains / Relative Speed

= 12 / 60 * 60 = 240 * 1 / 1000 / 2x

= 1 / 300 = 120 / 1000x

= x = 300 * 120 / 1000 = 36

Therefore The required speed = 36kmph.

6. Answer : (3) Rs. 18000

Explanation:

Let the incomes of P and Q be Rs. 3x and 4x respectively.

Again, let their expenditures be Rs. 2y and 3y respectively.

According to the question.

3x – 2y = 6000 …….(I)

and 4x – 3y = 6000 …….(II)

From equations (I) and (II)

3x – 2y = 4x – 3y

or, 4x – 3x = 3y – 2y

or, x = y

From equation (1)

3x – 2x = 6000

Therefore x = 6000

Therefore The income of P = Rs. 3x

= Rs. (3 * 6000)

= Rs. 18000

7. Answer : (2) 120

Explanation :

Ratio of values of 50 paise, 25 paise and 10 paise coins

= 2/2 : 3/4 : 5/10 = 1 : 3/4 : 1/2

= 4 : 3 : 2

Sum of the ratios = 4 + 3 + 2

= 9

Therefore Value of 25 paise coins

= 3 / 9 * 90 = Rs. 30

Therefore Number of 25 paise coins

= 30 * 4 = 120

8. Answer : (4) 9litres

Explanation :

Let the amount of water be x litres

Therfore x + 3 / x = 3 / 2

or, 2x + 6 = 3x or, x = 6

Therefore The quantity of spirit in the mixture = x + 3 = 6 + 3

= 9 litres

9. Answer : (1) Rs. 205.20

Explanation:

A single discount equal to the two successive discounts

= [ 10 + 5 – 10 * 5 / 100 ]%

= 14.5%

Therefore Selling price of the article

= 85.5 % of Rs. 240

= Rs. 85.5 * 240 / 100

= Rs. 205.20

10. Answer : (4) Rs. 27.5 per kg.

Explanation:

Let the original rate be Rs. x per kg.

Reduced Rate

= Rs. (100 – 20) * 1 / 100 x

= Rs. 4x / 5

Therefore 385 / 4x / 5 – 385 / x = 3.5

or, 385 [ 5 / 4x – 1 / x] = 3.5

or 385 / 4x = 3.5

or, x = 385 / 4 * 3.5 = 27.5

Therefore original rate = Rs. 27.5 per kg.