Important for :

1

D

Let a two-digit number be (10x + y) and reversing number be (10y + x)

Hence, it's divisible by 11.

Hence, option D is correct.

Hence, option D is correct.

2

D

Let the greater number be x and smaller number be yand x = 4y ..... (ii)

From eqs. (i) and (ii)

4y – y = 45

⇒ y = | 45 | = 15 |

3 |

On putting the value of y in Eq. (ii), we get

x = 4 × 15 = 60

Hence, required sum = x + y = 60 + 15 = 75.

Hence, option D is correct.

3

C

Let the number be y,∴ | y | = | y | + 8 ⇒ | 4y – 3y | = 8 |

3 | 4 | 12 |

⇒ y = 12 × 8 = 96

Hence, option C is correct.

4

B

Let the fare from station P to station Q is ₹ x and the fare from station P to station R is ₹ y.

By given condition, x + y = 42 .....(i)

and 5x + 10y = 350 .... (ii)

On solving Eqs. (i) and (ii), we get

x = 14 and y = 28

Hence, fare from station P to station Q is ₹ 14.

Hence, option B is correct.

Hence, option B is correct.

5

B

6x – 5y = 13 ...... (i)7x + 2y = 23 ...... (ii)

By equation (i) × 2 & (ii) × 5,

12x – 10y = 26 ..... (iii)

35x + 10y = 115 ...... (iv)

by solving these equation we get

x = 3, y = 1

Hence, option B is correct.