Arithmetic(Exams > Cat > Quantitaitve Aptitude ) Questions and answers for exam Preparation

Exams > Cat > Quantitaitve Aptitude

ARITHMETIC MCQs

Total Questions : 147 | Page 15 of 15 pages

A tub is filled with a mixture of 2 miscible fluids P and Q in the proportion 5:3. When 16 litres of the mixture is drawn off and the tub is filled with same amonut of fluid Q, the proportion becomes P:Q=3:5. How many litres does the tub hold___

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Answer: Option A. ->
:

Let the tub contain 5x litres of P and 3x litres of Q. total = 8x litres of mixture. When are taken out, (8x-16) litres will be left

The mixture will now contain $\frac{5}{8} (8 x - 16) = 5 (x - 2)$ litres of P and 3(x-2) litres of Q.

Given that 16 litres of Q are added.

Ratio is given as
$\frac{5 (x - 2)}{3 (x - 2) + 16} = \frac{3}{5}$

Solving we get x-2=3 ; x=5

Tub will hold 8x = 40 litres

Question 142.

C and D are the children of A $&$ B, who are married to each other. D is 5 years younger than C. Five years ago, A was twice as old as C. The current age of B is the average of A and C’s ages. If the average age of all of them is 34 years, find the current age of D?

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Answer: Option C. -> 22
:
C

Let the present age of each of them be the letters themselves.

Present age of D= C-5

Presnt age of A will be 2(C-5)+5

=2C-5 and the present age of B will be $\frac{C + 2 C - 5}{2} = \frac{(3 C - 5)}{2}$

Average age of members =34

$C + C - 5 + 2 C - 5 + \frac{(3 C - 5)}{2} = 34 \times 4$

$4 C + \frac{(3 C - 5)}{2} = 146$

11C= 297

C=27

D= 27-5=22

Option (C)

Question 143.

Dexter is coming up with a chemical complex using 3 different soluble substances in the volume ratio 3:4:7. The densities of these substances are in the ratio 5:2:6 respectively. The mass of the $2^{n d}$ substance contained in 130 litres of the complex is ___

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Answer: Option C. -> 22
:

$D e n s i t y = \frac{M a s s}{V o l u m e}$

Individual volume ratio = volume of component

Total volume

Ratio of volumes $= \frac{3}{14} : \frac{4}{14} : \frac{7}{14}$

Ratio of densitites $= \frac{5}{13} : \frac{2}{13} : \frac{6}{13}$

Ratio of masses $= \frac{3}{14} \times \frac{5}{13} : \frac{4}{14} \times \frac{2}{13} : \frac{7}{14} \times \frac{6}{13} = 15 : 8 : 42$ . mass in $2^{n d}$ substance $= \frac{8}{65} \times 130 = 16$ litres.

Question 144.

Fresh grapes contain $90 %$ water by weight and dry grapes contain $20 %$ water by weight. The weight of dry grapes obtained from 20 kg of fresh grapes is (in kg., in decimal, up to 2 decimal places) ___

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Answer: Option C. -> 22
:

20 kg $\to 10 %$ (non water content) = 2kg
2 = $80 %$ (non water content dry grapes)
$\Rightarrow$ wt = 2.50 kg

Question 145.

At a gold shop’s annual promotion, gold coins are distributed with each purchase.The higher the purchase, the higher the value of the gold coin. The value of the gold coin is directly proportional to the thickness and square of the diameter of the coin.Two gold coins are given to a customer. The value of coin1: coin 2 = 4:1. The diameter of the coins are in a ratio 4:3. Find the ratio of the thickness of the coins?

9 : 6
11 : 7
9 : 4
12 : 5

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Answer: Option C. -> 9 : 4
:
C

$\frac{T h i c k n e s s_{1} \times d i a_{1}^{2}}{T h i c k n e s s_{2} \times d i a_{2}^{2}} = \frac{4}{1} \frac{T h i c k n e s s_{1}}{T h i c k n e s s_{2}} = \frac{4}{1} \times \frac{9}{16} = \frac{9}{4}$

Question 146.

In Little flowers school, for a school drill, the students are divided into 2 groups of lilies and daisies.The ratio of lilies: daisies = 8:3. The ratio of boys: girls is 7:4. $60 %$ of the daisy group is boys.
What is the difference in the number of boys who are in the lily group and the number of girls in the daisy group, given that there are 48 girls in the daisy group?

200
240
160
None of these

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Answer: Option C. -> 160
:
C

1.2X is given as 48 hence x will be 40.

So the number of boys in lilies will be $5.2 \times 40 = 208$

So the difference will be 208 - 48 = 160

Question 147.

In Little flowers school, for a school drill, the students are divided into 2 groups of lilies and daisies.The ratio of lilies: daisies = 8:3. The ratio of boys: girls is 7:4. $60 %$ of the daisy group is boys.
What is the ratio of the number of girls in the lily group and the number of boys in the Daisy group ?

20 :13
11:20
14:9
Cannot be determined

Discuss Question

Answer: Option C. -> 14:9
:
C