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Q:

The value of $(l o g_{5} (5)) (l o g_{4} (9)) (l o g_{3} (2)) i s :$

A) 1	B) 3/2
C) 2	D) 5

Answer & Explanation Answer: A) 1

Explanation:

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Filed Under: Logarithms

Q:

If $l o g_{\sqrt{8}} (x) = 3 \frac{1}{3} t h e n f i n d t h e v a l u e o f x ?$

A) 25	B) 32
C) 37	D) None of these

Answer & Explanation Answer: B) 32

Explanation:

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Q:

$T h e v a l u e o f l o g_{2} (l o g_{5} (625)) i s :$

A) 2	B) 5
C) 10	D) 15

Answer & Explanation Answer: A) 2

Explanation:

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Filed Under: Logarithms
Exam Prep: Bank Exams , CAT
Job Role: Bank Clerk

Q:

The value of $l o g_{343} (7) i s :$

A) 1/3	B) -3
C) -1/3	D) 3

Answer & Explanation Answer: A) 1/3

Explanation:

$\log_{343} (7) \log_{7^{3}} (7) \frac{1}{3} \log_{7} (7) W e k n o w t h a t l o g_{x} (x) = 1 = > \frac{1}{3}$

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Filed Under: Logarithms
Exam Prep: AIEEE , Bank Exams , CAT
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Q:

Tea worth of Rs. 135/kg & Rs. 126/kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be____?

A) Rs. 169.50	B) Rs.1700
C) Rs. 175.50	D) Rs. 180

Answer & Explanation Answer: C) Rs. 175.50

Explanation:

Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135)/2= Rs.130.50

So, Now the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say Rs. 'x' per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find 'x'.

Cost of 1 kg tea of 1st kind Cost of 1 kg tea of 2nd kind

x-153/22.50 = 1 => x - 153 = 22.50 => x=175.50.

Hence, price of the third variety = Rs.175.50 per kg.

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Filed Under: Alligation or Mixture
Exam Prep: CAT , Bank Exams , AIEEE

Q:

8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16 : 65. How much wine the cask hold originally?

A) 18 litres	B) 24 litres
C) 32 litres	D) 42 litres

Answer & Explanation Answer: B) 24 litres

Explanation:

Let the quantity of the wine in the cask originally be x litres

Then, quantity of wine left in cask after 4 operations = $[x {(1 - \frac{8}{x})}^{4}]$ litres

$∴ [\frac{x {(1 - \frac{8}{x})}^{4}}{x}] = \frac{16}{81}$

$\Rightarrow {[1 - \frac{8}{x}]}^{4} = {(\frac{2}{3})}^{4}$

$\Rightarrow x = 24$

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Filed Under: Alligation or Mixture

Q:

The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is

A) Rs. 19.50	B) Rs. 19
C) Rs. 18	D) Rs. 18.50

Answer & Explanation Answer: C) Rs. 18

Explanation:

Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have :

Cost of 1 kg of type 1 rice Cost of 1 kg of type 2 rice

$∴$ (20-x)/(x-15) = 2/3

$\Rightarrow$ 60 - 3x = 2x - 30

$\Rightarrow$ x = 18.

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Q:

A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?

A) 10	B) 20
C) 21	D) 25

Answer & Explanation Answer: C) 21

Explanation:

Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively

Quantity of A in mixture left = $(7 x - \frac{7}{12} \times 9) = (7 x - \frac{21}{4})$ litres.

Quantity of B in mixture left = $(5 x - \frac{5}{12} \times 9) = (5 x - \frac{15}{4})$ litres.

$\frac{(7 x - \frac{21}{4})}{(5 x - \frac{15}{4}) + 9} = \frac{7}{9}$

$\Rightarrow \frac{28 x - 21}{20 x + 21} = \frac{7}{9}$

$\Rightarrow x = 3$

So, the can contained 21 litres of A.

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Filed Under: Alligation or Mixture

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