1

2

C

Let the number be x, y and z.

Then x + y = 45 ....(i) y + z = 55 ....(ii) z + 3x = 90 .... (iii)

Now, from (i)

y = 45 – x

And from (ii) z = 55 – y

z = 10 + x

Putting the value of z in equn. (iii) , we have

3x + 10 + x = 90

y = 45 – 20 = 25 and z = 10 + 20 = 30.

Hence, option C is correct.

Hence, option C is correct.

3

A

No. of observations = 6, Increased average = 1.5, Total increased = 6 × 1.5 = 9

Now, let the unit digit of the number whose digits have been interchanged = x and ten's digit of the number = y

Original number = (10y + x), Number after interchanging the digits = (10x + y)

So, (10x + y) – (10y + x) = 9 OR 9x – 9y = 9

For such questions you can refer to the table below

Difference in no. after interchanging the digits | Difference in the digits of the original no. |

9 (9 × 1) |
1 |

18 (9 × 2) | 2 |

27 (9 × 3) | 3 |

36 (9 × 4) |
4 |

Hence, option A is correct.

4

5

A

Then, x(x + 1) = 7482

or, x

or, x

or, (x + 87)(x – 86) = 0

Hence, the greater positive integer is 87.

Calculate square root of 7482 = 86.49

Therefore, the first no. will be 86 & the larger no. be (86 + 1) = 87

PS: Apply the shortcut method to find square root of 7482.

Hence, option A is correct.

Hence, option A is correct.