Q1. Perimeter of a square is 24 cm and length of a rectangle is 8 cm. If the perimeters of the square and the rectangle are equal, then the area (in square cm) of the rectangle is
(a) 16
(b) 24
(c) 32
(d) 64
Sol.
Perimeter of rectangle = Perimeter of square
Perimeter of rectangle = Perimeter of square
2(l=b)=24
2(8+b)=24 (∵l=8 cm)
2b=8
∴b=4 cm
∴ Area of rectangle = l×b=8×4=32〖cm〗^2.
Q2. The speed of a boat in a river is 20 km per hour and the speed of another boat is 23 km per hour. They travel in the same direction from the same place at the same time. The distance between the boats after three and half hours is
(a) 10 km
(b) 10.5 km
(c) 11 km
(d) 11.5 km
Sol.
Distance travelled by first boat
Distance travelled by first boat
= Speed × time = 20×3 1/2=20×7/2
= 70 km
Distance travelled by second boat
=23×3 1/2=23×7/2=80.5 km
Distance between the boats = 80.5 – 70 = 10.5 km.
Q3. When a fresh fish is dried it becomes 1/3 of its weight. Sunita buys 1500 kg fresh fish for Rs. 80 per kg. How much does she earn?
(a) Rs. 2,500
(b) Rs. 2,700
(c) Rs. 3,000
(d) Rs. 3,500
Sol.
C.P of fresh fish = 1500 × 25 = Rs. 37500
C.P of fresh fish = 1500 × 25 = Rs. 37500
Weight of dried fish = 1/3×1500=500 kg.
S.P. of dried fish = 500×80 = Rs. 40000
Profit earned by Sunita = 40000 – 37500
= Rs. 2500
Q4. 750 ml juice is filled in one bottle and six such bottles are packed in one carton. The number of cartons needed for 450 liters of juice is
(a) 75
(b) 80
(c) 90
(d) 100
Sol.
Number of cartons required
Number of cartons required
=(450×1000)/(750×6)=100
(∵1 litre=1000 ml)
Q5. Internal length, breadth and depth of a (rectangular) box are 4 cm, 3 cm and 2 cm respectively. How many such boxes are needed to pack 8664 centimeter cubes?
(a) 351
(b) 361
(c) 391
(d) 722
Sol.
Number of rectangular boxes required
Number of rectangular boxes required
=8644/(4×3×2)=361
Q6. The difference between the smallest common multiple and biggest common factor of 5, 10 and 35 is
(a) 30
(b) 35
(c) 65
(d) 75
Sol.
Smallest common multiple i.e.
Smallest common multiple i.e.
LCM of 5, 10 and 35 = 70
Biggest common factor i.e.,
HCF of 5, 10 and 35 = 5.
Difference between LCM and HCF = 70 – 5 = 65
Q7. Number of degrees in three and one half right angles is
(a) 285
(b) 295
(c) 305
(d) 315
Sol.
Three and one half right angles
Three and one half right angles
=3 1/2×90°=7/2×90°=315°
Q8. The perimeter of a square is 20 cm. A rectangle has the same width as the square. The length of the rectangle is double its width. The area, in square cm, of the rectangle is
(a) 30
(b) 50
(c) 100
(d) 25
Sol.
Perimeter of Square = 20 cm
Perimeter of Square = 20 cm
Let side of Square = x cm
Therefore, 4x=20
x=5 cm
Width of rectangle = 5 cm
Length of rectangle = 2×5=10 cm
Area of rectangle = 10×5=50 cm^2
Q9. The internal length, breadth and height of a rectangular box A are 20 cm, 18 cm and 15 cm respectively and that of box B are 18 cm, 12 cm and 5 cm respectively. The volume of box A is how many times that of box B?
(a) 4
(b) 5
(c) 6
(d) 3
Sol.
Volume of box A = 20 cm ×18 cm ×15 cm
Volume of box A = 20 cm ×18 cm ×15 cm
Volume of box B = 18 cm ×12 cm ×5 cm
Now, (Volume of box A)/(Volume of box B)=(20 × 18 × 15)/(18× 12 × 5)
= 5
Q10. One orange costs five and half rupees and one kg apple costs Rs. 80. Then the total cost of one and half dozen of oranges and one and three-fourth kg of apples is
(a) Rs. 219
(b) Rs. 229
(c) Rs. 239
(d) Rs. 209
Sol.
Total cost = 18 oranges + 1.75 kg apples
Total cost = 18 oranges + 1.75 kg apples
=18×5.5+1.75×80=99+140=239
