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GATE Questions

A) 1/12 | B) 2/14 |

C) 1/14 | D) 2/13 |

Explanation:

Ans. C.

Let 4 consecutive even numbers are x, x+ 2, x+ 4, x+ 6

According to the question -

1/x + 1/x+2 = 11/60

x+2+x/ x(x+2) = 11/60

2(x+1)/x^2 + 2x = 11/60

120x + 120 = 11x 2 + 22x

11x 2 - 98x – 120 = 0

So ,

X = -24/22 , 10

X = -12/11 , 10

So, the numbers will be 10,12,14,16.

Hence,

Third largest number = 14

Reciprocal of third number = 1/14

A) 5740 | B) 5720 |

C) 5620 | D) 5730 |

Explanation:

Ans. B.

According to the question ,

Marked Price = 1600 + Cost price - (i)

MP – 500 = 125/100 * CP - (ii)

MP = 5/4 CP + 500 - (ii)

4MP = 5CP + 2000 -(ii)

Solving (i) and (ii)

Cost Price = 4400

Now , the selling price

= 130/100 * 4400

= 5720

A) 21/3 days | B) 48 days |

C) 40 days | D) 48/5 days |

Explanation:

Ans.

Time taken by A to complete a work alone - 24 days

Time taken by A in completing 1/3 of work = 24*1/3= 8 Days

8 day = time taken by B in completing 1/2 of work

B alone can complete the work = 16 days

The required time in completing the work if both A & B start working together?

16*24 / 40 = 48/5 Days

A) 900km | B) 940km |

C) 960km | D) 980km |

Explanation:

Ans.

Distance covered by 1st train in 4 hours = 80*4 = 320 km

Relative speed of 2nd train = 120-80 = 40 km

It will overtake another train in 320/40 = 8 hours

Distance between overtake point and station A = 8*120 = 960 km

A) 6000 | B) 7000 |

C) 5000 | D) 8000 |

Explanation:

Ans.

Let B’s investment = x rs.

∴ A’s investment =( x + 1200) rs.

Ratio of the profits of A and B = (x+1200)*(15+4):x*15 = {19(x+1200)}:15x

Now,let the total profit of A =y

∴ total profit of B = (y-280)

But total profit = 1240

⇒y+(y-280)=1240

⇒2y=1520

⇒y= 760

∴profit of A = 760rs.

Profit of B = 760-280=480 rs.

Ratio of profits= 760:480 = 19:12

According to the question,

19(x+1200)/15x = 19/12

12x+14400 = 15x

⇒3x = 14400

⇒x = 4800 rs.

⇒investment of A = 4800+1200

= 6000 rs.

A) 3:2 | B) 2:3 |

C) 5:7 | D) 7:5 |

Explanation:

Ans. Let radius of the base and height of the cone be ‘r’ & ‘h’ respectively.

Then volume of cone = πr2h/3 For cylinder, radius is reduced by 4 times = r/4 And, height is increased by 8 folds = 8h Volume of cylinder = πR2H = π(r/4)2 (8h) = (16/8)πr2h = πr2h/2 Ratio of volume of cone to volume of cylinder = (πr2h/3) : (πr2h/2) Or, Ratio = 2 : 3.

A) If only conclusion I follow. | B) If only conclusion II follow. |

C) If either conclusion I or conclusion II follows. | D) If neither conclusion I nor II follows. |

Explanation:

K > R = L, P > L, R ≥ S

L = R ≥ S**Conclusions:**

I. S < L

II. L = S

This forms a complementary pair - S is either smaller or equal to L. Hence, the correct option is Either conclusion I or conclusion II follows.