Q1. The ratio of the prices of two flates P and Q was 5 : 7 last year. This year, the price of P is increased by 20 per cent and that of Q by Rs. 45,000. If their prices are now in the ratio 9 : 11, the price of Q last year was:
(a) Rs. 9,60,000
(b) Rs. 9,45,000
(c) Rs. 9,80,000
(d) Rs. 8,00,000
Q2. One fashion designer group has to make 720 dresses and another one 840 dresses during the same period of time. In the first group the order was ready 4 days ahead of time and in the second group, 8 days ahead of time. How many dresses did each fashion designer group make a day if the second fashion designer group made 20 dresses more a day than the first?
(a) 54 and 75
(b) 24 and 48
(c) 40 and 60
(d) 44 and 25
Q3. There were 52 students in a hostel. Due to the admission of 16 new students, the expenses of the mess increases by Rs. 44 per day while the average expenditure per head diminished by Rs. 4. What was the original expenditure of the mess?
(a) Rs. 1027
(b) Rs. 1107
(c) Rs. 1050
(d) Rs. 850
Q4. Six years ago, the ages of the members of a joint family of six people added up to 168 years. Four years later, one member died at the age of 54 years and a child was born during the same year. After another four years, one more member died, again at 54 and a child was born during the same year. The current average age of this six-member joint family is nearest to:
(a) 22 years
(b) 20 years
(c) 25 years
(d) 24 years
Q5. A boy was asked of his age by his teacher. The boy said, ‘The number you get when you subtract 28 times my age from thrice the square of my age will be seven times of your age.’ If the teacher’s age is 28, then the age of the boy is:
(a) 28 years
(b) 21 years
(c) 14 years
(d) 25 years
Q6.A train travels a distance of 192 km at an average speed of 80 km/h from station P to another station Q. It then travels back to P taking 5 hours 36 minutes. Find the average speed of the train during its journey from P to Q and Q to P.
(a) 72 km/h
(b) 36 km/h
(c) 48 km/h
(d) 60 km/h
Q7.In eleven hours C walks 12.5 km less than what D does in twelve hours; and in five hours D walks 3.25 km less than what C does in seven hours. How many km does each walk per hour?
(a) 3 and 4
(b) 3.5 and 4.25
(c) 2.33 and 3.4
(d) 3.25 and 4.5
Q8.A two-digit number exceeds by 19 than sum of the squares of its digits and by 44 than double product of its digits. Find the number.
(a) 83
(b) 62
(c) 38
(d) 72
Q9.A heap of topaz, rubies and emeralds is required to be formed. A topaz is worth Rs 5crores, a ruby Rs 2 crores and an emerald Rs 3 crores. The weight of a topaz is 0.7 kg, weight of a ruby is 0.2 kg and that of an emerald is 0.3kg. If the total weight allowed is 8 kgs, then which of the following combination maximizes the worth of the entire heap?
(a) 10 topaz, 2 rubies, 2 emeralds
(b) 6 topaz, 1 ruby, 12 emeralds
(c) 11 topaz, 1 emerald
(d) 26 emeralds, 1 ruby
Q10.Anam bought a jute bag at 30% discount on the list price. He then sold it at a price which is 160% of the list price thereby making a profit of Rs 81. What is the list price of the bag?
(a) Rs 90
(b) Rs 100
(c) Rs 180
(d) Rs 200
Solutions:
S1. Ans.(b)
Sol.
Let prices of flates P and Q were Rs. 5x and Rs. 7x respectively in previous year.
∴(5x×120/100)/(7x+45,000)=9/11
⇒ 66x = 63x + 4,05,000
⇒ x = Rs. 1,35,000
∴ Price of Q in last year = Rs. 9,45,000
S2. Ans.(c)
Sol.
Let first fashion designer group makes x dress in a day.
∴ second will make (x + 20) dresses in a day
Let total time was t days.
∴ x (t – 4) = 720 …(i)
And (x + 20) (t – 8) = 840 …(ii)
Solving (i) and (ii) we get
t = 22 days
∴ x = dresses made by first group = 40
and that by second group = 60
S3. Ans.(a)
Sol.
Let expenses per student was Rs. x
∴ 68(x – 4) – 52x = 44
⇒ 16x = 316
⇒ x = 19.75
∴ Original expenditure = 52 × 19.75
= Rs. 1027
S4. Ans.(d)
Sol.
Current average of age
=1/6×(168+36 –54+24 –54+24)
= 24 years
S5. Ans.(c)
Sol.
Let boy’s age = x years.
ATQ,
3x² – 28x = 7 × 28
⇒ 3x² – 28x – 196 = 0
⇒ 3x² – 42x + 14x – 196 = 0
⇒ x = 14 years
S6. Ans.(c)
Sol.
Average speed =(Total distance travelled)/(Total time taken)
=(192×2)/(192/80+5.6)
= 48 km/h
S7. Ans.(b)
Sol.
Let C walks x km per hour and D walks y km per hour
∴ 12y – 11x = 12.5 …(i)
And,
7x – 5y = 3.25 ..(ii)
Solving (i) and (ii) we get
x = 3.5 km per hour
y = 4.25 km per hour
S8. Ans.(d)
Sol.
Let, unit’s place and ten’s place digits be y and x respectively.
Hence, number = 10x + y
According to the question,
10x + y – 19 = x^2 + y^2 …(i)
10x + y – 44 = 2xy …(ii)
Now from options,
Only one number (72) satisfies the both the equations.
Required answer = 72
S9. Ans.(d)
Sol.
From option (a), total worth = 10× 5 + 2 × 2 +2 × 3
= 60 crores
From (b), total worth = 6 × 5 + 1 × 2 + 12 × 3
= 68 crores
From (c), total worth = 11 × 5 + 3
= 58 crores
From (d) total worth = 26 × 3 + 1 × 2
= 80 crores
S10. Ans.(a)
Sol.
Let list price of bag = Rs x
∴160/100 x-70/100 x=81
⇒ x = Rs. 90
