86) The LCM of two numbers is 20 times their HCF, and the sum of the LCM and the HCF is 504. If the difference of the numbers is 24, then find the sum of the numbers.
A) 210
B) 180
C) 225
D) 216
Explanation:We are given:
* LCM = 20 × HCF
* LCM + HCF = 504
* Difference of the numbers = 24
* We need to find the sum of the two numbers
—
Let HCF = 
Then LCM = 
So:
Now:
* HCF = 24
* LCM = 
—
Let the two numbers be 
and 
(Since HCF is 24, both numbers are multiples of 24)
Also,
And the difference of numbers is:
24a – 24b = 24 ⇒ a – b = 1
Now:
a – b = 1, ab = 20
Use these to solve for 
and 
:
From 
Substitute into 
:
So the numbers are:
24a = 24×5 = 120, 24b = 24×4 = 96
⇒ Sum = 120 + 96 = 216
—
✅ Correct Answer: 4. 216
87) The present average age of X, Y and Z is 44 years. 8 years ago the average age of X and Y was 38 years. What is the present age of Z?
A) 39 years
B) 38 years
C) 41 years
D) 40 years
Explanation:We are given:
* Present average age of X, Y, Z = 44 years
⇒ Total = 
years
* 8 years ago, average age of X and Y = 38 years
⇒ Total age of X and Y 8 years ago = 
So, present total age of X and Y =
76 + 8×2 = 76 + 16 = 92
Now, present age of Z =
88) Who became the first Indian female athlete to win two individual Olympic medals?
A) Mirabai Chanu
B) Dutee Chand
C) PV Sindhu
D) Ankita Raina
89) In a certain code language, ‘RICE’ is coded as ‘5136’, ‘FUR’ is coded as ‘327’, and ‘FIN’ is coded as ‘785’. How will FUN’ probably be coded in that language?
A) 258
B) 182
C) 872
D) 718
90) In each of the given number-clusters, the number on the right side of (the equal to sign)is calculated by performing certain mathematical operations on the three numbers on the left of = (the equal to sign). All three number-clusters follow the same pattern. Select the number from among the given options that can replace the question mark (?) in the third number-cluster.
21, 9, 40 =149
18, 7, 25 =101
15, 11, 30=?
A) 110
B) 120
C) 125
D) 135