Directions : Study the following questions carefully and choose the right answer.
Important for :
1
A mixture contains mango juice and water in the ratio 9 : 5 respectively. 28 litres of the mixture is replaced by water. Now the ratio of Mango juice and water became 18 : 17. Find the quantity of mango juice in the initial mixture.
» Explain it
A
Let the quantity of mango juice and water in the initial mixture is 9x litres and 5x litres respectively.

Quantity of mango juice in 28 litres mixture

 = 9 × 28 = 18 litres 14

Quantity of water in 28 litres mixture
 = 5 × 28 = 10 litres 14

 9x – 18 = 18 5x – 10 + 28 17

 ⇒ 9x – 18 = 18 5x + 18 17

⇒ 153x – 306 = 90x + 324

⇒ 63x = 324 + 306

 ⇒ x = 630 63

⇒ x = 10

Quantity of mango juice in initial mixture = 9x = 9 × 10 = 90 litres.

Hence, option (A) is correct.

2
A and B together can complete a piece of work in 12 days, B and C together can complete a piece of work in 16 days, A and C together can complete a piece of work in 24 days. Find the number of days in which A, B and C together can complete the work.
» Explain it
B

 1 + 1 = 1 A B 12

 1 + 1 = 1 B C 16

 1 + 1 = 1 A C 24

Adding all the above equations, we get
 2 ( 1 + 1 + 1 ) = 1 + 1 + 1 A B C 12 16 24

 ⇒ 2 ( 1 + 1 + 1 ) = 4 + 3 + 2 A B C 48

 ⇒ 1 + 1 + 1 = 9 A B C 96

 ⇒ 1 + 1 + 1 = 3 A B C 32
Hence, A, B and C together can complete the work in 32/3 days.

Smart approach:

Total work = LCM of 12, 16 and 24 = 48
 Efficiency(A + B) = 48 = 4 12

 Efficiency(B + C) = 48 = 3 16

 Efficiency(A + C) = 48 = 2 24

2 × Efficiency(A + B + C) = 9
 Efficiency(A + B + C) = 9 2

Required number of days
 = 48 = 96 = 32 days 9/2 9 3

Hence, option (B) is correct.

3
A shopkeeper marks his article in such a way that even after allowing 18% discount on marked price, he gains 28%. If the cost price of the article is Rs.246, find the marked price of the article.
» Explain it
B
mp × (100 – %d) = cp × (100 + %p)

⇒ mp × (100 – 18) = 246 × (100 + 28)

 ⇒ mp = 246 × 128 82

⇒ mp = Rs.384

Hence, option B is correct.
4
In how many different ways letters of the word “EDUCATION” can be arranged such that all the consonants come together?
» Explain it
C
Number of consonants = 4

Consonants can be arranged among themselves in 4! Ways.

E, U, A, I, O and (DCTN) can be arranged in 6! Ways

Required number of ways = 6! × 4! = 720 × 24 = 17280

Hence, option (C) is correct.

5
Average of a set of five consecutive even numbers is 48. Average of another set of five consecutive odd numbers is 49. Find the product of smallest even number of the first set and largest odd number of the second set.
» Explain it
D
Average of n consecutive even/odd numbers

⇒ a = first number + (n – 1)

⇒ 48 = first number + (5 – 1)

⇒ first number = 44

Even numbers are: 44, 46, 48, 50, 52

And

a = first number + (n – 1)

⇒ 49 = first number + (5 – 1)

⇒ first number = 45

Odd numbers are: 45, 47, 49, 51, 53

Required product = 44 × 53 = 2332

Hence, option (D) is correct.

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