# Mixed Quantitative Aptitude Questions Set 207

1. In what ratio water be mixed with orange juice to earn a profit of 20 % by selling the mixture at cost price?

5 : 2
5 : 1
5 : 4
5 : 3
5 : 2
Option B
Let the cost price of juice be Rs. 1

Selling price of mixture = Rs. 1

Cost price of mixture = 1 * 100/120 = 5/6
juice water
1 0
5/6
0-5/6 : 5/6-1

= > – (5/6) : – (1/6)

= > 5 : 1

2. 2) A bag contains x black marbles and 5 pink marbles. If the probability of taking 2 pink marbles is 5/33, then find the number of black marbles?

8
4
5
6
7
Option E
Let the number of black marbles be x,

Probability = 5C2/(x+5)C2 = 5/33

(5 * 4) /[(x + 5)(x + 4)]= 5/33

132 = (x + 5) (x + 4)

x2 + 9x + 20 = 132

x2 + 9x – 112 = 0

(x + 16) (x – 7) = 0

x = -16, 7 (Negative value will be eliminated)

So, x = 7

The number of balck marbles = 7

3. 3) Incomes of Rekha and Amir are in the ratio 4 : 5 and their expenditures are in the ratio 6 : 7. If Rekha and Amir saves Rs. 4000 and Rs. 8000 respectively, then find the income of Rekha?

Rs. 40000
Rs. 50000
Rs. 10000
Rs. 20000
Rs. 30000
Option A
Incomes of Rekha and Amir are in the ratio = 4 : 5 (4x, 5x)

= > (4x – 4000)/(5x – 8000) = 6/7

= > 28x – 28000 = 30x – 48000

= > 2x = 20000

= > x = 10000

Income of Rekha = 4x = Rs. 40000

4. 4) A Boat takes 2 hours less to travel to 80 Km downstream than to travel the same distance upstream. If the speed of the stream is 10 Km/hr, then find the speed of boat in still water?

30 km/hr
70 km/hr
50 km/hr
20 km/hr
10 km/hr
Option A
Let the speed of boat in still water be x,

According to the question,

2 = 80/(x – 10) – 80/(x + 10)

2 = 80 * [1/(x – 10) – 1/(x + 10)]

1 = 40 * [(x + 10 – x + 10) / (x2 – 100)]

x2 – 100 = 40 * 20

x2 = 800 + 100 = 900

x = 30

The speed of boat in still water = 30 km/hr

5. How many 4 letter words with or without meaning can be formed out of the letters of the word, “FLIPKART”, if repetition of letters is not allowed?

1610
1650
1620
1680
1600
Option D
“FLIPKART”, contains 8 different letters.

Required number of words = 8p4

= > (8 * 7 * 6 * 5) = 1680

6. In each of the following questions, a question is followed by three statements I, II and III. Read all the statements to find the answer to given question and then answer accordingly that which statements can give the answer alone/together.
Find the probability of drawing three marbles of different colours from the box.

I. The box contains only three different coloured marbles red, white and blue.

II. Probability of drawing one red marle from the bag is ¼.

III. Probability of drawing one blue marble from the box is 1/3.

All I, II and III
Any two of the three
Only I and III
Any one of the three
Even I, II and III together are not sufficient.
Option E
Let, red = x

White = y

Blue = z

From I:

The box contains only three different coloured marbles red, white and blue.

From II:

Probability of drawing one red marble from the box is ¼.

From III:

Probability of drawing one blue marble from the box is 1/3.

From I, II and III:

x/(x + y + z) = ¼

=> 4x = x + y + z

=> 3x – y – z = 0

And

z/(x + y + z) = 1/3

=> 3z = x + y + z

=> x + y – 2z = 0

Since, there are three variables, we need three equations to solve the question.

Hence, even I, II and III together are not sufficient.

7. Rahul deposits some amount in a bank.Find the difference between the compound interest and simple interest on that sum after two years at the rate of r% per annum.

I. The sum amounts to Rs.44100 on compound interest at 5% per annum after two years.

II. Simple interest on Rs.25000 at r% per annum after four years will be Rs.8000.

III. The sum amounts to Rs.59200at 8% per annum after six years.

All I, II and III
Any two of the three
Only I and III
Any one of the three
Even I, II and III together are not sufficient.
Option D
Amount on CI = P x (1 + r/100)t

=> 44100 = P x (1 + 5/100)2

=> 44100 = P x 105/100 x 105/100

=> P = 44100 x 100/105 x 100/105

=> P = Rs.40000

And

We know that

SI = (P x r x t)/100

8000 = (25000 x r x 4)/100

=> 8000 = 1000 x r

=> r = 8%

We know that, for two years

CI – SI = P x (r/100)2

= 40000 x (8/100)2

= 40000 x (2/25)2

= 40000 x 4/625

= Rs.256

From II and III:

We know that

SI = (P x r x t)/100

8000 = (25000 x r x 4)/100

=> 8000 = 1000 x r

=> r = 8%

And

Amount on SI = (P x r x t)/100 + P

=> 59200 = (P x 8 x 6)100 + P

=> 59200 = 48P/100 + P

=> 59200 = (48P + 100P)/100

=> 59200 = 148P/100

=> P = 592000 x 100/148

=> P = Rs.40000

We know that, for two years

CI – SI = P x (r/100)2

= 40000 x (8/100)2

= 40000 x (2/25)2

= 40000 x 4/625

= Rs.256

Hence, Only II and either I or III are sufficient

8. 5) Usha, Trisha and Jaisha entered into a partnership for three years. Find the share of Usha in the profit.

I. Usha, Trisha and Jaisha invested in the ratio 8:4:5. After one year Tina doubled her investment.

II. At the end of three years, they earned a total profit of Rs.80000.

III. After two years, Jaisha doubled her investment.

All I, II and III
Any two of the three
Only I and III
Any one of the three
Even I, II and III together are not sufficient.
Option A
From I:

Usha, Trisha and Jaisha invested in the ratio 8:4:5. After one year Trisha doubled her investment.

From II:

At the end of three years, they earned a total profit of Rs.80000.

From III:

After two years, Jaisha doubled her investment.

From I, II and III:

Let, amounts invested by Usha, Trisha and Jaisha be Rs.8k, Rs.4k and Rs.5k respectively.

Ratio of share in the profit:

Usha : Trisha : Jaisha = (8k x 3) : (4k + 8k x 2) : (5k x 2 : 10k)

= 24k : 20k : 20k

= 6 : 5 : 5

Share of Usha in the profit = 6/(6 + 5 + 5) x 80000

= 6/16 x 80000

= Rs.30000

Hence, all I, II and III together are sufficient.

9. The ratio of the ages of A and B before six years was 13:11. Respective ratio of the age of B before four years and age of B after four years will be 3:4. Respective ratio of the present ages of B and C is 7:6. Find the difference between the present ages of A and C.

8 years
7 years
6 years
4 years
5 years
Option A
Let, ages of A and B before six years be 13k and 11k respectively.

According to the question

(11k + 2)/(11k + 10) = 3/4

=> 44k + 8 = 33k + 30

=> 44k – 33k = 30 – 8

=> 11k = 22

=> k = 2

Present age of A= 13k + 6 = 13 x 2 + 6 = 32 years

Present age of B = 11k + 6 = 11 x 2 + 6 = 28 years

Present age of C = 6/7 x 28 = 24 years

Required difference = 32 – 24 = 8 years

10. The ratio of the salary of Mani, Prem, Nila and Kani is 6:4:5:3 and respective ratio of their savings is 4:3:5:2. Expenditure of Mani is (200/3) % of his income. Expenditure of Nila is what percent of her income?

30%
60%
55%
40%
50%
Option E
Let, income of Mani, Prem, Nila and Kani be Rs.6x, Rs.4x, Rs.5x and Rs.3x respectively.

Now, Expenditure of Mani = ((200/3)/100) * 6x = 4x

Let, expenditure of Nila be Rs.k

According to the question

(6x – 4x) / (5x – k) = 4/5

=> 2x/(5x – k) = 4/5

=> 10x = 20x – 4k

=> 4k = 20x – 10x

=> k = 10x/4

=> k = 2.5x

Required percentage = 2.5x/5x * 100

= 50%

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