# Splification - Quantitative Aptitude

Q11. Hari paid 3/5 of a bill. If Rs. 600 of the bill is still due, what was the total amount of the bill ?

(a) Rs. 1100

(b) Rs. 1300

(c) Rs. 1500

(d) Rs. 1700

**Answer:** (c) Rs. 1500

Let, the total amount of the bill be Rs. x

Paid bill = Rs. x X (3/5) = Rs. 3x/5

Due bill = Rs. (x - (3x/5)) = Rs. 2x/5

A/Q 2x/5 = 600 ⇒ x = (600 X 5)/2 = Rs. 1500

Q12. After measuring 120 meters of a rope it was discovered that the metre rod was 3 cm longer. The true length of the rope measured is

(a) 123.60 m

(b) 126.55 m

(c) 129.34 m

(d) 133.25 m

**Answer:** (a) 123.60 m

If measured length 1m, true length = 1.03 m

∴ If measured length 120m, true length = 1.03 X 120 = 123.60 m

Q13. A bag contains three types of coins - rupee coin, 50p coins and 25p coins, totalling 175 coins. If the total value of the coins of each kind the same, the total amount in the bag is

(a) Rs. 60

(b) Rs. 75

(c) Rs. 80

(d) Rs. 88

**Answer:** (b) Rs. 75

Let, the value of each kind of coins be Rs. x

Number of coins = x + 2x + 4x = 7x

A/Q 7x = 175

⇒ x = 25

Total amount = Rs. (25 + 25 + 25) = Rs. 75

Q14. How many 1/8 's are there in 37½ ?

(a) 250

(b) 300

(c) 325

(d) 375

**Answer:** (b) 300

Required Number = 37½ ÷ 1/8 = (75/2) X 8 = 75 X 4 = 300

Q15. If (2a + b) = 6 and ab = 4, then (1/a + 2/b) = ?

(a) 1/2

(b) 1/4

(c) 3/2

(d) 3/4

**Answer:** (c) 3/2

1 | + | 2 | = | b + 2a | = | 6 | = | 3 |

a | b | ab | 4 | 2 |

Q16. A part of monthly expenses of a family is constant and remaining varies with the price of wheat. When the rate of wheat is Rs. 250 per quintal, the total monthly expenses of the family are Rs. 1000 and when it is Rs. 240 per quintal, the total monthly expenses are Rs. 980. The total monthly expenses of the family when the cost of wheat is Rs. 350 per quintal are

(a) Rs. 850

(b) Rs. 900

(c) Rs. 1050

(d) Rs. 1200

**Answer:** (d) Rs. 1200

Let C be the constant expenditure and x quintal wheat is consumed

Now C + 250x = 1000 ------ (1)

and C + 240x = 980 -------- (2)

(1) - (2) ⇒ 10x = 20

⇒ x = 2

(1) ⇒ C + 250 X 2 = 1000

⇒ C = 1000 - 500 = 500

Required expenses = Rs. (500 + 350 X 2) = Rs. 1200

Q17.

(469 + 174)^{2} - (469 - 174)^{2} |
= ? |

469 X 174 |

(a) 4

(b) 7

(c) 9

(d) 11

**Answer:** (a) 4

469^{2} + 2 X 469 X 174 + 174^{2} - 469^{2} + 2 X 469 X 174 - 174^{2} |

469 X 174 |

= | 4 X 469 X 174 |

469 X 174 |

= 4

Q18.

1/2 . 1/2 . 1/2 + 1/5 . 1/5 . 1/5 - 3 . 1/2 . 1/5 . 1/7 + 1/7 . 1/7 . 1/7 | = ? |

1/2 . 1/2 + 1/5 . 1/5 + 1/7 . 1/7 - (1/2 . 1/5 + 1/5 . 1/7 + 1/2 . 1/7) |

(a) 33/55

(b) 37/62

(c) 47/69

(d) 59/70

**Answer:** (d) 59/70

a^{3} + b^{3} + c^{3} - 3abc |

a^{2} + b^{2} + c^{2} - (ab+bc+ca) |

= | a^{3} + b^{3} + c^{3} - 3abc |

a^{2} + b^{2} + c^{2} - ab - bc -ca |

= a+b+c

= 1/2 + 1/5 + 1/7

= | 35 + 14 + 10 |

70 |

= | 59 |

70 |

Q19. A man has in all Rs. 640 in the denominations of one rupee, five rupee and ten rupee notes. The number of each types of notes are equal. What is the total number of notes he has ?

(a) 105

(b) 120

(c) 135

(d) 150

**Answer:** (b) 120

Let, the number of notes be x of each types

Now x + 5x + 10x = 640

⇒ 16x = 640

⇒ x = 40

∴ Total number of notes = 3x = 3 X 40 = 120

Q20. If (x+y)^{2} - z^{2} = 3, (y+z)^{2} - x^{2} = 7, (z+x)^{2} - y^{2} = 26, then (x+y+z) = ?

(a) 6

(b) 11

(c) 13

(d) 15

**Answer:** (a) 6

(x+y)^{2} - z^{2} = 3

⇒ (x+y+z)(x+y-z) = 3

⇒ x+y-z = 3/(x+y+z) ------- (1)

Again (y+z)^{2} - x^{2} = 7

⇒ (y+z+x)(y+z-x) = 7

⇒ y+z-x = 7/(x+y+z) ------- (2)

(z+x)^{2} - y^{2} = 26

⇒ (z+x+y)(z+x-y) = 26

⇒ z+x-y = 26/(x+y+z) -------- (3)

(1)+(2)+(3)⇒ x+y+z = | 3 | + | 7 | + | 26 | = | 3+7+26 | = | 36 |

x+y+z | x+y+z | x+y+z | x+y+z | x+y+z |

⇒ (x+y+z)^{2} = 36

⇒ x+y+z = 6

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