The sum of the ages of 3 people A, B and C is 90 years. What would be the total of their ages 4 years back?
A. 74 years
B. 78 years
C. 86 years
D. 80 years
Option: B Explanation: Required sum = (90 - 3 x 4) years = (90 - 12) years = 78 years.
Two bus tickets from city Amb to Sunhet and three tickets from city Amb to Dehra cost Rs. 77 but three tickets from city Amb to Sunhet and two tickets from city Amb to Dehra cost Rs. 73. What are the fares for cities Sunhet and Dehra from Amb?
A. Rs. 4, Rs. 23
B. Rs. 13, Rs. 17
C. Rs. 15, Rs. 14
D. Rs. 17, Rs. 13
Option: B Explanation: Let Rs. x be the fare of city Sunhet from city Amb and Rs. y be the fare of city Dehra from city Amb.
So, we will get the equations
Then, 2x + 3y = 77 ... (i) and
3x + 2y = 73 ... (ii)
Multiplying (i) by 3 & (ii) by 2 & subtracting, we get: 5y = 85 or y = 17.
Putting y = 17 in (i), we get: x = 13.
Bulls Eye a premier institute organized a sports meet for its students where 1/5 of the girls and 1/8 of the boys participated. What was the total fraction of the students who had actually taken part?
D. Data inadequate
Option: D Explanation: In this question, we do not have the actual number of boys and girls.
Therefore, we cannot find the fraction of the total students who participated.
Some friends planned on a leisure trip where they had planned Rs.96 on eatables. 4 of them did not come. So the rest of them had to pay Rs. 4 each extra. The number of people who turned up on the trip was
Option: A Explanation: Let the number of persons be x. Then
(96 / x - 4)- (96/x) = 4
⇔ (1 / x - 4) - 1 / x = 4 / 96
⇔ x - ( x - 4 ) / x ( x - 4 ) = 1 / 24
⇔ x2 - 4x - 96 = 0
⇔ ( x - 12) (x + 8) = 0
⇔ x = 12
So, required number = x - 4 = 8
Akbar, Birbal, Chaitanya, David & Ehasaan play a game of coins. Akbar says to Birbal, "If you give me 30 coins, you will have as many as Ehsaan has and if I give you 30 coins, you will have as many as David has." Akbar and Birbal together have 100 coins more than what David and Ehsan together have. If Birbal has 20 coins more than what Chaitanya has and the total number of coins that they have is 1330, how many coins does Birbal have?
Option: C Explanation: Clearly, we have :
Birbal-30 = Ehsaan ...(i)
Birbal + 30 = David ...(ii)
Akbar+Birbal = David+Ehsaan+100 ...(iii)
Birbal = Chaitanya + 20 ...(iv)
Akbar+Birbal+Chaitanya+David+Ehsaan= 1330 ...(v)
From (i) and (ii), we have : 2 Birbal=D+E ...(vi)
From (iii) and (vi), we have : Akbar=Birbal + 100 ...(vii)
Using (iv), (vi) and (vii) in (v), we get:
(Birbal + 100) + Birbal + (Birbal - 20) + 2(Birbal) = 1330
5(Birbal) = 1250
Birbal = 250
Cost of a pineapple will be Rs. 7 each whereas a watermelon will cost Rs. 5 each. A man spends a total of Rs. 38 on these fruits. The number of pineapples that he purchased were:
D. Data inadequate
Option: C Explanation: Let the number of pineapples and watermelons be x and y respectively.
Then, 7x + 5y = 38 or 5y = (38 - 7x) or y = 38 - 7x / 5
Clearly, y is a whole number, only when (38 - 7x) is divisible by 5.
This happens when x = 4.
Nikhil says, "If you reverse the digits in my age, the number that you will obtain will be Salil's age. Salil is older than me and the difference of ages of me & Salil will be one-eleventh of the sum of our ages." The age of Nikhil is
A. 23 years
B. 34 years
C. 45 years
D. None of these
Option: C Explanation: Let 'p' and 'q' be the ten's and unit's digits respectively of the number which denotes the age of Nikhil's age.
Then, Nikhil's age = (10p + q) years; Salil's age = (10q + p) years.
Therefore (10q + p)- (10p + q) = (1/11) (10q + p + 10p + q)
(9q-9p) = (1/11)(11q + 11p) = (p+ q)
10p = 8q
p = (4/5)q
So, q should be a multiple of 5 and also should be a single digit, which is 5.
So the values obtained will be, p = 4, q = 5.
Hence, Nikhil's age = 10p+ q = 45 years.
A circle is circumscribed about an equilateral triangle, and that equilateral triangle is circumscribed about another circle. Then the ratio of perimeter of circumcircle to that of an incircle is
A. 3 : 4
B. 1 : 2
C. 2 : 1
D. 4 : 3
Option: C Explanation: Let the side of an equilateral triangle is 'a'. Then radius of a circumcircle is a/√3 and radius of an incircle is a/2√3. The ratio of perimeter is a/√3 : a/2√3 = 2 : 1
Anu had a total of Rs. 320 in the denominations of 1-rupee coins, 5-rupee coins & 10-rupee coins. Given that the number of coins for all the denominations is same. What is the total no. of coins that he has?
Option: B Explanation: Let the number of coins of each denomination be x. Then, x + 5x + 10x = 320 ⇔ 16x = 320 ⇔ x = 20. Hence, total number of coins = 3x = 60.
What will be the product of all the numbers on a telephone?
D. None of these
Option: D Explanation: One of the numbers on the telephone will be zero which gives us the product of all the numbers as zero.