Q1. Chintu, Pintu and Mintu are three friends. Chintu is twice as old as Pintu and Mintu is as old as Cintu and Pintu together. Two years later, the ratio of age of Chintu and Mintu would be 7:10 what was the age of Pintu five years ago?

A. 2 years B. 4 years C. 5 years D. 1 years E. 8 years

Answer - Option D
Explanation - Let Pintu’s present age = x, Chintu = 2x and Mintu = x + 2x = 3x
Two years later [latex][\frac{2x+2}{3x+2}][/latex] = [latex](\frac{7}{10})[/latex]
20x + 20 = 21x + 14
x = 6
Pintu’s present age = 6
Five years ago, his age was 6 - 5 = 1 year
Q2. In a school, students of class I and class II are going for a picnic to Surajkund and Badkal lake respectively. The ratio f number of students in class I and II is 5:3. Also the ratio of the contribution made by each student of class I and II is 19:17. If the total contribution made by the all the students of both the class is Rs.29200, then find the total contribution made by class II students only

A. Rs.10950 B. Rs.13789 C. Rs.10200 D. Rs.13272 E. None of these

Answer - Option C
Explanation - Let the no. of students in class II be 5x and 3x respectively and contribution made by each student of class I and class II be 19y and 17y respectively.
Hence, ratio of total contribution of class I and class II = 5x × 19y : 3x × 17y = 95 : 51
Total contribution made by students of class II ([latex]\frac{51}{(95+51)}[/latex]) × 29200 = 10200
Q3. A donkey moves at a speed of 8 kmph, when no load is put on him. Reduction in the speed of donkey varies directly to the square root of the kgs of load put on him. When only 4 kgs of load is put the speed of the donkey becomes 6 kmph. Find the minimum load that can be put on the donkey with which it cannot move.

A. 64 kg B. 63.9 kg C. 65.2 kg D. Cannot be determined E. None of these

Answer - Option A
Explanation - Speed of the donkey, Without any load = 8 kmph. With 4 kgs of load, speed becomes 6 kmph, hence speed is reduced by 2 kmph.
Reduction in speed varies directly with the square root of the load.
Hence (8 - 6) = k√4 = k ± 1
The donkey cannot move at zero speed. i.e. when his speed reduced by 8 kmph. So reduction in speed = 8 kmph
8 = 1√l => √l = 8 and l = 64, when √l = -8, l = 64
At 64 kg the donkey will stop.
Q4. A container has a mixture of kerosene and castor oil in the ratio of 7:5 and another container contains kerosene and castor oil in the ratio of 5:3. Find the proportion in which the mixtures from two containers should be mixed so that the resultant mixture has ratio of kerosene and castor oil of 3:2.

A. 2:3 B. 3:2 C. 4:1 D. 5:2 E. None of these

Answer - Option B
Explanation - Let quantity of mixture taken from first be x and second be y.
Amount of kerosene oil in the resultant mixture (x + y) is
([latex]\frac{7}{12}[/latex])x + ([latex]\frac{5}{8}[/latex])y = ([latex]\frac{3}{5}[/latex])(x + y)
([latex]\frac{7}{12}[/latex])x - ([latex]\frac{3}{5}[/latex])x = ([latex]\frac{3}{5}[/latex])y - ([latex]\frac{5}{8}[/latex])y - ([latex]\frac{1}{60}[/latex])x = -([latex]\frac{1}{40}[/latex])y => ([latex]\frac{x}{y}[/latex]) = ([latex]\frac{6}{4}[/latex]) = ([latex]\frac{3}{2}[/latex]) = 3 : 2
Q5. There are three vessels 1, 2 and 3. The ratio of the total capacity of vessels 1, 2 and 3 is 5:4:3 respectively. All the vessels are full of mixture of sugar syrup and water. In vessel 1, ratio of sugar syrup to water is 2:3. Similar ratio in case of vessel 2 and vessel 3 is 5:4 and 1:3 respectively. The mixture of all the three vessels is emptied into one bigger vessel. What is the resulting ratio of sugar syrup and water?

A. 17:25 B. 179:253 C. 253:179 D. 233:169 E. None of these

Answer - Option B
Explanation - Let the total mixture in vessel 1,2 and 3 be 5 litres and 3 litres respectively. So, quantity of water in (5 + 4 + 3) = 12 litres of mixture is
= ([latex]\frac{3}{5}[/latex])×5 + ([latex]\frac{4}{9}[/latex])×4 + ([latex]\frac{3}{4}[/latex])×3
= 3 + ([latex]\frac{16}{9}[/latex]) + ([latex]\frac{9}{4}[/latex]) = ([latex]\frac{108+64+81}{36}[/latex]) = ([latex]\frac{253}{36}[/latex])
Quantity of sugar syrup is
12 - ([latex]\frac{253}{36}[/latex]) = ([latex]\frac{179}{36}[/latex])
Ratio of sugar syrup to water = 179 : 253

Q1. A particular sum was divided among A, B and C in ratio 2:6:7 respectively. If the amount received by A was Rs. 4,908, what was the difference between the amounts received by B and C?

A. Rs. 2,454 B. Rs. 3,494 C. Rs. 2,135 D. Rs. 2,481 E. None of these

Answer - Option A
Explanation - If the total amount be Rs. x, then ([latex]\frac{2x}{15}[/latex]) = 4908
x = [latex]\frac{(4908 × 15)}{2}[/latex] = Rs. 36810
Required difference = ([latex]\frac{(7 – 6)}{15}[/latex]) × 36810 = Rs. 2454
Q2. The average age of a man and his son is 30 years. The ratio of their ages four years ago was 10:3 respectively. What is the difference between the present ages of the man and his son?

A. 28 years B. 16 years C. 26 years D. 44 years E. None of these

Answer - Option A
Explanation - Four years ago,
Father’s age = 10x years , son’s age = 3x years
10x + 3x + 8 = 60 (sum of their ages = 2 × 30 = 60)
= 13x = 60 – 8
= x = 4
Required difference
Q3. The ratio between Gloria’s and Sara’s present ages is 4:7 respectively, Two years ago the ratio between their ages was 1:2 respectively. What will be Sara’s age three years hence?

A. 17 years B. 14 years C. 11 years D. 8 years E. None of these

Answer - Option A
Explanation - Let Gloria’s and Sara’s present ages be 4x and 7x years respectively
Two years ago, [latex]\frac{(4x – 2)}{(7x – 2)}[/latex] = [latex]\frac{1}{2}[/latex]
8x – 4 = 7x – 2
x = 2
Sara’s age three years hence = 7x + 3 = 17 years
Q4. The total number of students in a school is 31700. If the ratio of boys to the girls in the school is 743:842 respectively, what is the total number of girls in the school?

A. 14860 B. 16480 C. 15340 D. Cannot be determined E. None of these

Answer - Option E
Explanation - .Boys : Girls = 743 : 842
Total number of students = 31700
Number of girls = ([latex]\frac{842}{(743 +842)}[/latex]) × 31700 = ([latex]\frac{842}{1585}[/latex]) × 31700
= 16840
Q5. A sum of Rs. 10,980 is to be divided amongst A, B and C in the ratio 7:3:5 respectively. How much is C’s share?

A. Rs. 3,600 B. Rs. 3,006 C. Rs. 3,650 D. Rs. 3,660 E. Rs. 3,124

Answer - Option D
Explanation - C’s share = ([latex]\frac{5}{15}[/latex]) × 10980 = Rs. 3660

Q1. In a class of 60 students, where the girls are twice that of boys. Kamal ranked seventeenth from the top. If there are 9 girls ahead of Kamal, the number of boys in rank after him is:

A. 3 B. 7 C. 12 D. 13 E. None of these

Answer - Option C
Explanation - Girls : Boys = 2 : 1. Total no.of students is 60
Girls 60 × ([latex]\frac{2}{3}[/latex]) = 40 and boys = 20. Kamal has been ranked 17 which means there are 16 students before him of which 9 are girls remaining 7 are boys.
7 boys are ahead of Kamal + Kamal is the 8[latex]^{th}[/latex] boy, hence, there are (20 – 8) = 12 boys after him.
Q2. Two varieties of rice at Rs. 10 per kg and Rs. 12 per kg are mixed together in the ratio 1 : 2. What is the price of the resulting mixture?

A. Rs. 10.50 per kg B. Rs. 10.67 per kg C. Rs. 11.20 per kg D. Rs. 11.33 per kg E. None of these

Answer - Option D
Explanation - Let the amount of rice be 1 kg and 2 kg. (The given ratio is 1 : 2). So, total cost = 10 × 1 + 12 × 2 = 10 + 24 = 34
Rs. 34 is the cost of (1 + 2 = 3) kg of rice.
Cost per kg = ([latex]\frac{34}{3}[/latex]) = 11.33 per kg
Q3. The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 25% of the girls are scholarship holders, then the percentage of the students who did not get scholarship is:

A. 68% B. 78% C. 82% D. 72% E. None of these

Answer - Option B
Explanation - Number of students in school = 100 (let)
Boys = ([latex]\frac{3}{5}[/latex]) × 100 = 60, Girls = 40
Students who did not get scholarship
Boys = 60 × ([latex]\frac{80}{100}[/latex]) = 48
Girls = 40 × ([latex]\frac{75}{100}[/latex]) = 30
Students who do not get scholarship = 78
Required percentage = 78
Q4. In a mixture of 60 litres, the ratio of acid and water is 2 : 1. If the ratio of acid and water is to be 1 : 2, then the amount of water (in litres) to be added to the mixture is

A. 50 B. 45 C. 55 D. 60 E. None of these

Answer - Option D
Explanation - In 60 litres of mixture,
Acid = ([latex]\frac{2}{3}[/latex]) × 60 = 40 litres, Water = 20 litres
If x litres of water be mixed, then ([latex]\frac{40}{(20 + x)}[/latex])= 80
x = 80 – 20 = 60 litres
Q5. Salaries of Akash, Babloo and Chintu are in the ratio of 2 : 3 : 5. If their salaries were increased by 15%, 10% and 20% respectively, what will be the new ratio of their salaries?

A. 3 : 3 : 10 B. 23 : 33 : 60 C. 20 : 22 : 40 D. Cannot be determined E. None of these

Answer - Option B
Explanation - .Required ratio = ([latex]\frac{(2 × 115)}{100}[/latex]) : ([latex]\frac{(3 × 110)}{100}[/latex]) : ([latex]\frac{(5 × 120)}{100}[/latex]) 230 : 330 : 600 = 23 : 33 : 60