Quantitative Aptitude Shortcut Tricks and Methods for Competitive Exam

Shortcut Tricks and Methods of Quantitative Aptitude:

Q.8. A rectangular tin sheet is 12 cm long and 5 cm broad. It is rolled along its length to form a cylinder by making the opposite edges just to touch each other. Then, the volume of the cylinder is 

Solution

Here, length of the rectangular in sheet = 12

And breadth of the rectangular tin sheet = 5 cm

When the rectangular sheet is rolled along its length into a cylinder so that the width of the sheet becomes the height of the cylinder, then the length of the sheet equals the circumference of the base of the cylinder.

i.e., 2πr = 12

r = 12/2π = 6/π cm and height, h = 5 cm

⸫ Volume of the cylinder = πr²h

= π(6/π)² × 5 = π × (36/π²)×5

= 180/π cm³

Q.9. A merchant advertise 10% off on the items bought from his store. The total discount got by a customer who bought a cooker worth 650, a heater worth 500 and a bag worth 65 is 

Solution

Here, cost of a cooker = Rs. 650

Cost of  heater = Rs. 500

And cost of a bag = Rs.65

Total cost = Rs.(650+500+65) = Rs. 1215

Discount = 10%

⸫ Net discount = Rs.(10% of 1215)

= Rs.[(10/100)*1215]

= 121.50

Q.10. What is a better investment 4% stock at Rs.120 or 3% stock at Rs.80? 

Solution

4% stock at Rs. 120 = 4% of 120

= (4/100)*120 = Rs. 4.80 and 3% Stock at Rs. 80 = 4% of 80

= (4/100)*120 = 4% of 80

= Rs. 2.40

It is clear that first investment is better

 Q.11. 20% raise of price followed by a discount of 25% of the raised portion will 

Solution

Let original cost of the object be Rs. 100

If 20% raised in price, then cost of the object = Rs.120

Cost increased = Rs.(120-100) = Rs 20

⸫ Discount on increased cost 

= 25% of 20 = (25/100)*20= 5

⸫ New cost = Rs. (120 – 5)

= Rs. 115.

Q.12. The sum of the ages of two brothers, having a different of 8 yr between them, will double after 10 yr. What is the ratio of the age of the younger brother to that of the elder brother?

Solution

Let the present age of two brother’s be x yr and (X+8) yr.

After 10 yr, Age of two brothers (X+10)

And (X+8+10)

According to the question,

X+10+X+18 = (X+X+8)*2

→ 2X+28=(2X+8)*2

→ 2(X+14)=(2X+8)*2

→ X+14 = 2X+8

→ X-2X = 8-14

→ -X = -6

→ X = 6

Q.13. The ratio of two numbers is 3:4 and their LCM is 180. The second number is 

Solution

Let the two number be 3x and 4x.

According to the question

12x = 180

X= 180/12=15

Thus, First number = 3*15 = 45 and

second number = 4*15=60

Q.14. A gun is fired at a distance of 1.34 km from Geeta. She hears the sound after 4 s. The speed at which sound travels is 

Solution 

Sound covers 1.34×1000 m distance in 4 s.

⸫ Speed of the sound = (1.34*1000)/4

= 1340/4=335 m/s

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