Directions : Read the following questions carefully and choose the right answer
Important for :
1
The ratio between a two-digit number and the sum of the digits of that number is 4 : 1. If the digit in the unit's is three more than the digit in the ten's places, what is the number?
» Explain it
B
Let the ten's digit be x. then, unit's digit =  (x + 3).

Sum of the digits = x + (x + 3) = 2x + 3.

Let the number  = 10x + (x +3) = 11x + 3

 So, 11x + 3 = 4 2x + 3 1

⇒  11x + 3  = 4(2x + 3)  ⇔  11x + 3  = 4 (2x + 3)

⇒  3x  =  9    ⇒   x  =  3

Hence, required number =  11x + 3  ⇒  36.

Hence, option B is correct.

2
Rahul gives a crystal diamond ring to his wife Vijeta on their wedding anniversary. However, the ring falls off Vijeta's hand and breaks into three pieces the weights of which are in the ratio of 2 : 3 : 4. The value of each piece is directly proportional to the square of their weights. The given value of the diamond in the ring was Rs. 24300. Find the loss due to breakage.
» Explain it
D
Ratio of each piece of diamond = 2x : 3x : 4x

∴   Solid crystal diamond = 2x + 3x + 4x = 9x

∴   Cost of solid crystal diamond = (9x)2 = 81x2

Cost of broken pieces of diamond = (2x)2 + (3x)2 + (4x)2 = 29x2

∴   Loss = 81x2 – 29x2 = 52x2

Given, 81x2 = 24300

 ∴   x2 = 24300 = 300 81

∴   Loss = 52 × 300 = Rs. 15600.

Hence, option D is correct.

3
A train leaves a station A at 7 am and reaches another station B at 11 am. Another train leaves B to 8 am and reaches A at 11:30 am. The two trains cross one another at
» Explain it
D
Kindly refer to the video or go through the explanation given below :

Let the distance between the stations A & B be 4 kms.

 ∴   Speed A → B = 4 = 1 km/hr 4

 & Speed B → A = 4 = 8 km/hr 7/2 7

Suppose they meet x hours after 8 am.

Distance covered by both the trains to meet each other = Distance covered by them from 8 am

 ( 1 + 8 ) × x = 3 kms                   (∵ Train A has already covered 1 km from 7 am to 8 am) 7

 ⇒ 15 x = 3 7

 ∴   x = 7 hr  = 1 hr 24 mins 5

∴  They will meet at 9 : 24 AM. (After adding 1 hr 24 mins to 8 am.)

Hence, option D is correct.
4
In the Mumbai Zoo, there are some ducks and some rabbits. If the head are counted there are 160, while the legs are 450. What will be numbers of Rabbit in the zoo?
» Explain it
A
Let, Ducks = x, Rabbit = y

As, Duck has 2 legs and rabbit has 4 legs,

2x + 4y = 450 ...1

x + y = 160

2x + 2y = 320 .... 2

Equation 1 – Equation 2

2y = 130

y = 65

Hence, option A is correct.
5
There are 50 students in a class. 40% of the students like Orange and 50% of the students like Mango. If 10 students like both of them, then how many students like either Orange or Mango or both of them?
» Explain it
B
The distribution of the fruits are given below:

The number students who like only Mangoes- 40% of 50 = 20

The number students who like only  Oranges- 50% of 50 = 25

n(A U B) = n(A) + n(B) – n(A ∩ B)

Therefore, the number of students who like either Orange or Mango or both of them = 20 + 25 – 10 = 35

Hence, option B is correct.
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