Q1. A dairy man pays Rs. 6.4 per litre of milk. He adds water and sells the mixture at Rs. 8 per litre, thereby making 37.5% profit. Find the proportion of the water to that of the milk received by the customers.
(a) 1 : 15 (b) 1 : 10 (c) 1 : 20 (d) 1 : 12 (e) None of these
Q2. Mr X mixed 10 kg of variety A rice with 15 kg of variety B rice and sold the mixture at a price 40% more than that of A. He did not get any profit. What is the ratio of the cost price of variety A to that of B per kg?
(a) 2 : 5 (b) 3 : 5 (c) 4 : 5 (d) 5 : 8 (e) None of these
Q3. A jar contains a mixture of two liquids A and B in the ratio 4 : 1. When 10 litres of the mixture is taken out and 10 litres of liquid B is poured into the jar, the ratio becomes 2 : 3. How many litres of liquid A was contained in the jar?
(a) 14 litres (b) 18 litres (c) 20 litres (d) 16 litres (e) None of these
Q4. A trader has 50 kg of rice, a part of which he sells at 10 percent profit and the rest at 5 percent loss. He gains 7 percent on the whole. What is the quantity sold at 10 percent gain and 5 percent loss?
(a) 30 kg, 10 kg (b) 40 kg, 15 kg (c) 35 kg, 40 kg (d) 40 kg, 10 kg (e) None of these
Q5. The wheat sold by agrocer contained 10% low quality wheat. What quantity of good quantity wheat should be added to 150 kg of wheat so that the percentage of low quality wheat becomes 5%?
(a) 85 kg (b) 50 kg (c) 135 kg (d) 150 kg (e) None of these
Q6. One type of liquid contains 25% of milk, the other contains 30% of milk. A container is filled with 6 parts of the first liquid and 4 parts of the second liquid. The percentage of milk in the mixture is:
(a) 27% (b) 31% (c) 29% (d) 33% (e) None of these
Q7. Two gallons of a mixture of spirit and water contain 12% of water. They are added to 3 gallons of another mixture, containing 7% of water and half a gallon of water is then added to the whole. Find the percentage of water in the resulting mixture.
(a) (17 + 3/11)% (b) (16 + 12/11)% (c) (14 + 1/11)% (d) (18 + 2/11)% (e) None of these
Q8. There are 2 bottles containing a mixture of wine, water and alcohol. The first bottle contains wine, water and alcohol in the ratio 3 : 5 : 2. The second bottle contains water and wine in the ratio 5 : 4. 1 litre of the first and 2 litres of the second are mixed together. What fraction of the mixture is alcohol?
(a) 1/15 litres (b) 6/13 litres (c) 2/15 litres (d) 6/19 litres (e) None of these
Q9. A bottle contains three-fourths of milk and the rest water. How much of the mixture must be taken away and replaced by an equal quantity of water so that the mixture has half milk and half water?
(a) 25% (b) (33 + 1/3)% (c) 45% (d) 50% (e) None of these
Q10. A bottle is full of dettol. One-third of it is taken out and then an equal amount of water is poured into the bottle to fill it. This operation is done four times. Find the final ratio of dettol and water in the bottle.
(a) 13 : 55 (b) 20 : 74 (c) 16 : 65 (d) 10 : 48 (e) None of these
Q11. An alloy of gold and silver weighs 50 g. It contains 80% gold. How much gold should be added to the alloy so that percentage of gold is increased to 90?
(a) 50 g (b) 60 g (c) 30 g (d) 40 g (e) None of these
Q12. Vijay purchased two different kinds of alcohol. In the first mixture, the ratio of alcohol to water is 3 : 4 and the second mixture it is 5 : 6. If he mixes, the two given mixtures and makes a third mixture of 18 litres in which the ratio of alcohol to water is 4 : 5, the quantity of the first mixture (whose ratio is 3 : 4) that is required to make 18 litres of the third kind of mixture is:
(a) 6 (b) 7 (c) 8 (d) 9 (e) None of these
Q13. An alloy contains only zinc and copper. One such alloy weighing 15 gm contains zinc and copper in the ratio of 2 : 3 by weight. If 10 gm of zinc is added then find what amount of copper has to be removed from the alloy such that the final alloy has zinc and copper in the ratio of 4 : 1 by weight?
(a) 5 gm (b) 5.5 gm (c) 6 gm (d) 4.8 gm (e) None of these
Q14. There are two alloys made up of copper and aluminum. In the first alloy copper is half as much as aluminum and in the second alloy, copper is thrice as much as aluminum. How many times the second alloy must be mixed with the first alloy to get the new alloy in which copper is twice as much as aluminum?
(a) 2 (b) 3 (c) 4 (d) 5 (e) None of these
Q15. A solution of sugar syrup has 15% sugar. Another solution has 5% sugar. How many litres of the second solution must be added to 20 litres of the first solution to make a solution of 10% sugar?
(a) 10 (b) 5 (c) 15 (d) 20 (e) None of these
S.P. = 8
Profit = 37.5%
C.P. = 8 x 100/137.5 = 64/11
10 : 1
Water:milk => 1 : 10
By allegation rule,
. 1.4 A
=> (1.4 A – A)/(B- 1.4 A) = (15/10) = 3/2
=> 2.8 A – 2A = 3B – 4.2A
=> 4.2A + 0.8A = 3B
=> A/B = 3/5
=> A : B = 3 : 5
Let quantity of A & B be 4x & x.
According to the question,[4x – 10 x (4/5)] / [((x – 10) x 1/5) + 10] = 2/3
=> 4x – 8/x + 8 = 2/3
=> 4x – 8 /x + 8 = 2/3
=> 12x – 24 = 2x + 16
=> 10x = 40
X = 4
Required answer = 4x = 4 x 4 = 16 litres
10% – 5%
=> 4 : 1
Required answer = 40 kg, 10 kg
Total Wheat = 150 kg
High quality = 135 kg
Low quality = 15 kg
(135 + x) /15 = 19/1
=> x = 150 kg
Let total capacity of container = 10
So,milk from first liquid = 6 x 25/100 = 1.5
So,milk from 2nd liquid = 4 x 30/100 = 1.2
Total milk = 1.5 + 1.2 = 2.7
Required answers = 2.7 /10 x 100 = 27%
First mixture, total = 2 gallon
Water = 2 x 12/100 = 0.24
2nd mixture, total = 3 gallon
Water = 3 x 7/100 = 0.21%
Total mixture = 2 + 3 + 1/2 = 11/2 gallon
Water = 0.24 + 0.21 + 0.50 = 0.95 gallon
Required answer = 0.95 x 100 / 5.5 = (17 + 3/11)%
Alcohol in 1 litre of first = 1 x 2/10 = 1/5
Alcohol in 2 litre of second = 2 x 0 = 0
Required answer = 1/5 x 3 = 1/15
Let total mixture = 4 litre
Milk = 3
Water = 1
And mixture to be taken away = x
Then, according to the question,[3 – (x X 3/4) ] /[ 1- (x/4) + x] = 1/1
=> 3 – 3x/4 = 1 + 3x/4
=> 6x/4 = 2
X = 8/6 =4/3
Required answer = 4/(3 x 4) x 100 = (33 + 1/3)%
Remaining dettol = 1 (1 – 1/3)4 = 16/81 part
So, required answer = 16 : 65
Gold in alloy = 50 x 80% = 40 gm
Silver in alloy = 50 x 20% = 10 gm
40 + x/10 = 90/10
=> x = 50 gm
By allegation rule,
=> 7 : 11
Required answer = 18 x 7/18 = 7 litres
1st alloy zinc = 2/5 x 15 = 6
Copper = 3/5 x 15 = 9
Let copper to be removed = x
6 + 10/9 – x = 4/1
=> 16 = 36 – 4x
=> x = 5 gm
Copper in 1st alloy = 1/3
Copper in 2nd alloy = 3/4
Copper in required alloy = 2/3
=> 1 : 4
Required answer = 4 times.
=> 1 : 1
So, required answer = 20 litres.
Directions (1-3): Read the following information carefully and answer the question below it.
In a certain code, ‘il be pee’ means ‘roses are blue’; ‘silk hee’ means ‘red flowers’ and ‘pee mit hee’ means ‘flowers are vegetables’.
Q1. How is ‘red’ written in that code?
(a) hee (b) silk (c) be (d) pee (e)None of the above
Q2.How is ‘roses’ written in that code?
(a) il (b) pee (c) be (d) silk (e) cannot be determined
Q3. How is ‘vegetables are red flowers’ written in this code?
(a) pee silk mit hee (b) silk pee hee be (c) il silk mit hee (d) silk pee hee il (e) cannot be determined
Directions (4-8): Read the following information carefully and answer the question below it.
In each of the Letter Analogy various terms of a letter series are given with one term missing as shown by (?). Choose the missing term out of the given alternatives.
Q4. HUA GTZ FSY ERX ?
(a) DWQ (b) DQW (c) WDQ (d) WQD (e) cannot be determined
Q5. DF GJ KM NQ RT ?
(a) UW (b) YZ (c) XZ (d) UX (e) None of the above
Q6. DCXW FEVU HGTS ?
(a) LKPQ (b) ABZ (c) JIRQ (d) LMRS (e) None of the above
Q7. AB DEF HIJK ? STUVWX
(a) MNOPQ (b) LMNOP (c) LMNO (d) QRSTU (e) None of the above
Q8. C G L R ?
(a) Y (b) S (c) U (d) Z (e) cannot be determined
Directions (9-10): Study the following information carefully and answer the questions given below:
In a certain code language ‘she can do this’ is written as ‘12 23 45 76’, ‘she know about that’ is written as ‘49 94 28 76’, ‘that can be fast’ is written as ‘67 28 45 84’ and ‘this is about care’ is written as ‘23 81 94 51’.
Q9. In the given code language what does the code ‘94’ stand for?
(a) care (b) about (c) know (d) Can’t be determined (e) None of the above
Q10. What is the code for ‘fast’ in the given code language?
(a) 84 (b) 67 (c) 45 (d) Either (a) and (b) (e) None of the above
Directions (11-15): Study the following information carefully and answer the questions given below:
In a certain code language,
Fake motion nor – *N6, @R3, #E4
not male fifth – *E4, @T3, #H5
mankind newly form – #M4, @Y5, *D7
Q11. What is the code for ‘motion’?
(a) #E4 (b) $R3 (c) *N6 (d) @N8 (e) Cannot be determined
Q12. Which of the following code can be coded for ‘NACTOR’?
(a) #D6 (b) @R6 (c) *S6 (d) @N6 (e) Cannot be determined
Q13. What is the code for ‘merge for neck?
(a) *E4 @H6 #M4 (b) #R3 *E4 @D5 (c) *M3 @H5 #E4 (d) #R3 @K4 *E5 (e) Cannot be determined
Q14. What is the code for ‘Fluent’?
(a) #F6 (b) $S5 (c) *S7 (d) #T6 (e) Cannot be determined
Q15. What is the code for ‘Nomenclature’?
(a) #P13 (b) #S11 (c) @E12 (d) @P11 (e) Cannot be determined
Sol. In the second and third statements, the common code word is ‘hee’ and the common word is ‘flowers’. So, ‘hee’ stand for ‘flowers’. Thus, in the second statement, ‘silk’ stands for ‘red’.
Sol. Since from the given information, we can only find the code for ‘are’ in the first statement, it cannot be determined which of the remaining two codes for ‘roses’.
Sol. Clearly, the required codes will consist of the same codes as in the third statements with the code for ‘red’ i.e. silk added to it.
Sol. All the letters of each term are moved one step backward to obtain the corresponding letters of the next term.
Sol. There is a gap of one letter between both the letters of first term, a gap of two letters between both the letters of second term and again a gap of one two letters between the letters of third and fourth terms respectively. Besides, the last letter of each term and the first letter of next term are in alphabetical.
Sol. First two letters of each term are in reverse order. Similarly third and fourth letters are also in reverse order. Besides, the second letter of each term is the letter next to the first letter of the proceeding term.
Sol. The number of letters in the term goes on increasing by 1 at each step. Each term consists of letters in alphabetical. The last letter of each term and the first letter of the next term are alternate.
Sol. There is a gap of three letters between the first and the second term, four letters between the second and the third term; and five letters between the third and the fourth term. So, there should be a gap of six letters between the fourth term and the missing term.
she can do this → 12 23 45 76 …(i)
she know about that → 49 94 28 76 …(ii)
that can be fast→ 67 28 45 84 …(iii)
this is about care→ 23 81 94 51 …(iv)
From (i) and (ii), she→ 76 …(v)
From (i) and (iii), can→ 45 …(vi)
From (i) and (iv), this→ 23 …(vii)
From (i), (v), (vi) and (vii), do→ 12 …(viii)
From (ii) and (iii), that → 28 …(ix)
From (ii) and (iv), about → 94 …(x)
From (ii), (v), (ix) and (x), Know→ 49 …(xi)
From (iii), (vi) and (ix), be/fast→ 67/84 …(xii)
From (iv), (vii) and (x), is/care→ 81/51 …(xiii)
Every symbol represents the first letter of each word in the following manner
# – F
@ – N
* – M
Every Letter in the code represents the last letter of the respective word.
Every number represent the total number of letters in the word.
Directions (1-10): In the following questions, a part of the sentence (a word or a phrase) has been highlighted in bold. four different ways of writing the word or phrase has been given in the options (b), (c), (d) and (e). Find the correct replacement of the given bold word or phrase. If the given word or phrase is grammatically correct, then select option (a). Option (a) repeats the same word or phrase.
Q1. Carnivorous mammals can endure what would otherwise be lethal levels of body heat because they have a heat-exchange network which kept the brain from getting too hot.
(a) which kept (b) that keeps (c) which has kept (d) that has been keeping (e) having kept
Q2. The commission has directed advertisers to restrict the use of the word “natural” to foods that do not contain color or flavor additives, chemical preservatives, or nothing that has been synthesized.
(a) or nothing that has been (b) or that has been (c) and nothing that is (d) or anything that has been (e) and anything
Q3. The Iroquois were primarily planters, but supplementing their cultivation of maize, squash, and beans with fishing and hunting.
(a) but supplementing (b) and had supplemented (c) and even though they supplemented (d) although they supplemnted (e) but with supplementing
Q4. As contrasted with the honeybee, the yellow jacket can sting repeatedly without dying and carries a potent venom that can cause intense pain.
(a) As contrasted with the honeybee, (b) In contrast to the honeybee’s, (c) Unlike the sting of the honeybee,
(d) Unlike that of the honeybee, (e) Unlike the honeybee,
Q5. None of the attempts to specify the causes of crime explains why most of the people exposed to the alleged causes do not commit crimes and, conversely, why so many of those not so exposed have.
(a) have (b) has (c) shall (d) do (e) could
Q6. The end of the eighteenth century saw the emergence of prize-stock breeding, with individual bulls and cows receiving awards, fetching unprecedented prices, and excited enormous interest whenever they were put on show.
(a) excited (b) it excited (c) exciting (d) would excite (e) it had excited
Q7. For members of the seventeenth-century Ashanti nation in Africa, animal-hide shields with wooden frames were essential items of military equipment, a method to protect warriors against enemy arrows and spears.
(a) a method to protect (b) as a method protecting (c) protecting (d) as a protection of (e) to protect
Q8. Scientists have recently discovered what could be the largest and oldest living organism on Earth, a giant fungus that is an interwoven filigree of mushrooms and rootlike tentacles spawned by a single fertilized spore some 10,000 years ago and extending for more than 30 acres in the soil of a Michigan forest.
(a) extending (b) extends (c) extended (d) it extended (e) is extending
Q9. Quasars, at billions of light-years from Earth the most distant observable objects in the universe, believed to be the cores of galaxies in an early stage of development.
(a) believed to be (b) are believed to be (c) some believe them to be (d) some believe they are
(e) it is believed that they are
Q10. Five fledgling sea eagles left their nests in western Scotland this summer, bringing to 34 the number of wild birds successfully raised since transplants from Norway began in 1975.
(a) bringing (b) and brings (c) and it brings (d) and it brought (e) and brought
Sol. The use of the past tense (kept) is incorrect because a current situation is discussed; the present tense (keeps) is consistent with the other verbs in the sentence. In (a) and (c), which introduces a restrictive clause. Some writers follow the convention that which can only be used for nonrestrictive clauses, but insistence on this rule is controversial, and both (a) and (c) can be rejected on other grounds.
Hence, B Correct. The verb keeps indicates a current situation and is consistent with the other verbs in the sentence. The sentence is clear and concise.
Sol. The use of ‘do not’ and ‘nothing’ in the same sentence creates a double negative and reverse the intended meaning. ‘Anything’ should be used instead of ‘nothing’. Logically, a “natural” food cannot contain any prohibited ingredient, so the list of prohibited ingredients must be connected by or.
D Correct. This sentence correctly avoids a double negative and uses parallel elements.
Sol. The participle supplementing would normally be expected to modify the first clause, describing or extending its meaning, but the logic of this sentence demands a contrast, not an extension. Consequently, the second part of the sentence must be revised to emphasize the contrast properly. The logic of the sentence also argues against a construction that would set the two clauses and the importance of their content equal when they clearly should not be. The best solution is to have the main clause describe the primary activity, and a subordinate clause, although they supplemented, describe the supplementary activity.
D Correct. Using although creates a subordinate clause in this sentence and logically links that clause with the main clause; the simple past supplemented parallels the simple past were.
Sol. The intent of the sentence is to contrast the honeybee and the yellow jacket. Correct idioms for such a contrast include in contrast with x, y, in contrast to x, y; and unlike x, y. In all these idioms, x and y must be grammatically and logically parallel. As contrasted with is not a correct idiom.
E Correct. This sentence uses a correct idiom, and the honeybee is properly parallel to the yellow jacket.
Sol. The sentence compares one group of people, most of the people exposed to the alleged causes, with another group of people, so many of those not so exposed. To maintain the comparison, the verb in the second part should match the verb in the first part. Since the first verb is do not commit, the second verb should be the parallel ‘do’. There is no need to repeat commit crimes since it is understood in this construction.
D Correct. This sentence correctly uses the verb ‘do’ to complete the comparison and maintain the parallelism with ‘do not commit’.
Sol. The bulls and cows are described in a series of participial phrases. Items in a series should be parallel: receiving awards is parallel to fetching unprecedented prices, but excited must be changed to exciting to make the third phrase, exciting enormous interest, parallel to the first two.
C Correct. In this sentence, exciting is parallel to receiving the fetching.
Sol. The bold part of the sentence begins a phrase describing items of military equipment. It is awkward and inaccurate to describe items themselves as a method. Replacing the bold phrase with the participle protecting creates a modifying phrase that clearly explains the purpose of the items of military equipment.
C Correct. In this sentence, protecting properly introduced a modifying phrase revealing the purpose of the items.
Sol. The original sentence is correctly written. The giant fungus is described as an interwoven filigree spawned … some 10,000 years ago and extending for more than 30 acres. The present participle extending parallels the past participle spawned.
A Correct. This sentence has the participles spawned and extending in a correct parallel construction. Spawned refers to something that happened in the past. Which extending refers to something that continues into the present.
Sol. The original sentence is not actually a sentence; it is a sentence fragment since it lacks a verb: believed to be on its own is a participial phrase. The verb ‘are’ must be placed before ‘believed to be’ to create a complete sentence.
B Correct. The verb believed to be grammatically completes the sentence and connects quasars to cores.
Sol. ‘Bringing’ is the present participle of the verb ‘to bring’. As used here, it correctly describes an action that happens at the same time as the action in the main clause; ‘bringing’ indicates that the number of wild birds became 34 when the five eagles left their nests.
A Correct. The participle bringing correctly links the two ideas in the sentence.