## Quantitative Aptitude Questions and Answers With Explanation (Practice set 18)

**Q1:****Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?**

A) 11 : 13 : 15 B) 11 : 13 : 17

C) 12 : 17 : 18 D) 12 : 15 :16

**Q2:****The length of a rectangle is twice its breadth if its length is decreased by 5cm and breadth is increased by 5cm, the area of the rectangle is increased by 75 sq cm. Find the length of the rectangle.**

A) 30 B) 40

C) 50 D) 60

**Q3:****How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS' if repetition of letters is not allowed?**

A) 4050 B) 3600

C) 1200 D) 5040

**Q4:****Three unbiased coins are tossed. What is the probability of getting at most two heads?**

A) 3/4 B) 7/8

C) 1/2 D) 1/4

**Q5:****How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3, and 4, if repetition of digits is allowed?**

A) 376 B) 375

C) 500 D) 673

**Q6:****The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750 sq.m. The length of the hall is**

A) 20 B) 25

C) 30 D) 35

**Q7:****On 8th Dec 2007, Saturday falls. What day of the week was it on 8th Dec 2006?**

A) Saturday B) Friday

C) Monday D) Tuesday

**Q8:****26 January 1950 which day of the week?**

A) Monday B) Wednesday

C) Thursday D) Tuesday

**Q9:****The average temperature for Monday, Tuesday, Wednesday, and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday were 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday?**

A) 34 B) 36

C) 38 D) 40

**Q10:****10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with an age difference of 2 years), the present average age of the family is the same. The present age of the youngest child is :**

A) 1 B) 2

C) 3 D) 4

**ANSWERS WITH EXPLANATION**

**Answer1: D) 12 : 15 :16****Explanation:**

Aman : Rakhi : Sagar = (70000 x 36) : (105000 x 30) : (140000 x 24) = 12 : 15 : 16.

**Answer2: B) 40****Explanation:**

let length = 2x and breadth = x then

(2x-5) (x+5) = (2x * x)+75

5x-25 = 75 => x=20

length of the rectangle = 40 cm

**Answer3: D) 5040****Explanation:**

'LOGARITHMS' contains 10 different letters.

Required number of words = Number of arrangements of 10 letters, taking 4 at a time.

= 10P4

= 5040.

**Answer4: B) 7/8****Explanation:**

Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}

Let E = event of getting at most two heads.

Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.

P(E) =n(E)/n(S)=7/8.

**Answer5: A) 376****Explanation:**

The smallest number in the series is 1000, a 4-digit number.

The largest number in the series is 4000, the only 4-digit number to start with 4.

The left-most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.

The next 3 digits (hundreds, tens, and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.

Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999.

Including 4000, there will be 376 such numbers.

**Answer6: C) 30****Explanation:**

Let breadth = x m

Then, length = (x+5)m

Area of a rectangle = Length x Breadth

x(x+5) = 750

x² + 5x - 750= 0

(x+30)(x-25)= 0

x = 25 or x = -30

Hence, breadth x = 25m

=> Length = x + 5 = 25 + 5 = 30m.

**Answer7: B) Friday****Explanation:**

The year 2006 is an ordinary year. So, it has 1 odd day.

So, the day of 8th Dec 2007 will be 1 day beyond the day of 8th Dec 2006.

But, 8th Dec 2007 is Saturday

S0, 8th Dec 2006 is Friday.

**Answer8: C) Thursday****Explanation:**

We know that,

Odd days --> days more than complete weeks

The number of odd days in 400/800/1200/1600/2000 years is 0.

Hence, the number of odd days in the first 1600 years is 0.

Number of odd days in 300 years = 1

Number of odd days in 49 years = (12 x 2 + 37 x 1) = 61 days = 5 odd days

Total number of odd days in 1949 years = 1 + 5 = 6 odd days

Now look at the year 1950

Jan 26 = 26 days = 3 weeks + 5 days = 5 odd days

Total number of odd days = 6 + 5 = 11 => 4 odd days

Odd days :-

0 = sunday ;

1 = monday ;

2 = tuesday ;

3 = wednesday ;

4 = thursday ;

5 = friday ;

6 = saturday

Therefore, Jan 26th 1950 was Thursday.

**Answer9: A) 34****Explanation:**

M + Tu + W + Th = 4 x 48 = 192

Tu + W + Th + F = 4 x 46 = 184

M = 42

Tu + W + Th = 192 - 42 = 150

F = 184 – 150 = 34

**Answer10: C) 3****Explanation:**

Total age of 4 members, 10 years ago = (24 x 4) years = 96 years.

Total age of 4 members now = [96 + (10 x 4)] years = 136 years.

Total age of 6 members now = (24 x 6) years = 144 years.

Sum of the ages of 2 children = (144 - 136) years = 8 years.

Let the age of the younger child be x years.

Then, the age of the elder child = (x+2) years.

So, x+(x+2) =8 <=> x=3

Age of younger child = 3 years.

**Also Practice:**** ****Quantitative Aptitude Questions and Answers With Explanation (Practice set 17)**