 Important for :
1
The cost of 1 dozen banana is Rs. 72 and the cost of one apple is 50% more than the cost of one banana. Anmol purchased x banana and (x + 4) apples and spent Rs. 186. Find the total number of fruits that he purchased.
» Explain it
C
 Cost of one banana = 72 = 6 Rs. 12
Cost of one apple = 6 × 150% = 9 Rs. According to the question, 6x + 9 (x + 4) = 186 6x + 9x + 36 = 186 15x = 186 – 36 15x = 150 x = 10 He purchased 10 bananas and 14 apples. Total fruits = 10 + 14 = 24 Hence, option C is correct.
2
If the numerator of a fraction is increased by 150% and the denominator of a fraction increased by 200%, fraction becomes 10/19. Find the fraction.
» Explain it
C
 Let fraction = x y

 x × 250% = 10 y × 300% 19

 250x = 10 300y 19

 x = 10 × 300 y 19 250

 x = 12 y 19

Hence, option C is correct.
3
The numerator of a fraction is decreased by 50% and the denominator is increased by 200%. If the resultant fraction is 5/2, find the 3/ 20th of the original fraction.
» Explain it
A
 Let the fraction = x y
According to the question,
 x – 50% of x = 5 y + 200% of y 2

 x – x 2 = 5 y + 2y 2

 2x – x 2 = 5 3y 2

 x = 5 6y 2

 ⇒ x = 30 = 15 y 2 1

3/ 20th of the original fraction = 15/ 1 × 3/ 20

= 9/ 4

Hence, option A is correct.
4
Sum of 4 consecutive even numbers is greater than three consecutive odd numbers by 81. If the sum of the least odd and even numbers is 59 then find the sum of largest odd and even numbers.
» Explain it
A
Method I:

Let 4 consecutive even numbers = x, x + 2, x + 4, x + 6

3 consecutive odd numbers = y, y + 2, y + 4

According to the question,

(x + x + 2 + x + 4 + x + 6) – (y + y + 2 + y + 4) = 81

4x + 12 – 3y – 6 = 81

4x – 3y = 75 .... 1

sum of least odd and even numbers = 59

x + y = 59 ....2

Equation 1 + (Equation 2 × 3)

7x = 252

x = 36

Least odd number = 59 – 36 = 23, least even number = 36

Largest even number = 36 + 6 = 42, Lagest odd number = 23 + 4 = 27

Sum = 42 + 27 = 69

Method II:

Let 4 consecutive even numbers = x, x + 2, x + 4, x + 6

3 consecutive odd numbers = y, y + 2, y + 4

sum of least odd and even numbers = 59

x + y = 59

Sum of the largest odd and even numbers = x + 6 + y + 4

= x + y + 10

= 59 + 10 = 69

Hence, option A is correct.
5
If the product of two consecutive even numbers is 5328, then what is the larger number?
» Explain it
B
Let the larger number be x

Then, smaller number = x – 2

Now, x(x – 2) = 5328

Or, x2 – 2x – 5328 = 0

Or, x2 – 74x + 72x – 5328 = 0

Or, x(x – 74) + 72(x – 74) = 0

∴   x = 74, –72

Therefore, the higher number = 74

Hence, option B is correct.

Intuitive Approach:

Option A: 64

Therefore, the smaller number must be 62, but we can infer that we won't be getting a number as big as 5328 even if we multiply 74 64 by 62. Option A thus gets eliminated.

Option B: 74

Therefore, the smaller number must be 72. Further, the product of the unit digits of both the smaller and the greater number is also 8 which matches that of the given product.

We can multiply and confirm whether it gives us the resultant number or not.

72 x 74 = 5328

It confirms that option B is the correct answer.

Option C: 72

If the larger number is 72, the smaller one must be 70. But if we multiply these two we'll get the unit digit as zero. Option C gets eliminated here.

Option D: 76

If the larger number is 76, the smaller one must be 74. But if we multiply these two, we'll get the unit digit as 4. Option D also gets eliminated.