Mathematics Mcqs

The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen?

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The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen?

A. Rs.32
B. Rs.28
C. Rs.36
D. Rs.25
E. None of these
Explanation:
Let the cost of each pen and pencil be ‘p’ and ‘q’ respectively.
16p + 8q = 352 — (1)
4p + 4q = 96
8p + 8q = 192 — (2)
(1) – (2) => 8p = 160
=> p = 20

the present average age of a couple and their daughter is 35 years. Fifteen years from now, the age of the mother will be equal to the sum of present ages of the father and the daughter. Find the present age of mother?

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the present average age of a couple and their daughter is 35 years. Fifteen years from now, the age of the mother will be equal to the sum of present ages of the father and the daughter. Find the present age of mother?

A. 43 years
B. 40 years
C. 48 years
D. 45 years
E. None of these
Explanation:
(f + m + d)/3 = 35
=> f + m + d = 105 — (1)
m + 15 = f + d
Substituting f + d as m + 15 in (1), we get
2m + 15 = 105
2m = 90 => m = 45 years.

Ten years ago, the age of Aftab was one-third the age of Kashif at that time. The present age of Kashif is 12 years more than the present age of Aftab. Find the present age of Aftab?

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Ten years ago, the age of Aftab was one-third the age of Kashif at that time. The present age of Kashif is 12 years more than the present age of Aftab. Find the present age of Aftab?

A. 14
B. 16
C. 18
D. 20
E. None of these
Explanation:
Let the present ages of Aftab and Kashif be ‘a’ and ‘b’ respectively.
a – 10 = 1/3 (b – 10) — (1)
b = a + 12
Substituting b = a + 12 in first equation,
a – 10 = 1/3 (a + 2) => 3a – 30 = a + 2
=> 2a = 32 => a = 16.

In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 18, find the number?

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In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 18, find the number?

A. 975
B. 753
C. 642
D. 684
E. None of these
Explanation:
Let the three digit numbers be 100a + 10b + c
a = b + 2
c = b – 2
a + b + c = 3b = 18 => b = 6
So a = 8 and b = 4
Hence the three digit number is: 864

The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?

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The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?

A. 49
B. 94
C. 83
D. Either (a) or (b)
E. None of these
Explanation:
Let the number be in the form of 10a + b
Number formed by interchanging a and b = 10b + a.
a + b = 13 — (1)
10b + a = 10a + b – 45
45 = 9a – 9b => a – b = 5 — (2)
Adding (1) and (2), we get
2a = 18 => a = 9 and b = 4
The number is: 94.

The sum of five consecutive even numbers of set x is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set x?

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The sum of five consecutive even numbers of set x is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set x?

A. 248
B. 240
C. 228
D. 236
E. None of these
Explanation:
Let the five consecutive even numbers be 2(x – 2), 2(x – 1), 2x, 2(x + 1) and 2(x + 2)
Their sum = 10x = 440
x = 44 => 2(x – 2) = 84
Second least number of the other set = 2(84) – 121 = 47
This set has its least number as 46.
Sum of the numbers of this set = 46 + 47 + 48 + 49 + 50
= 48 – 2 + 48 – 1 + 48 + 48 + 1 + 48 + 2 => 5(48) = 240

In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?

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In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?

A. 8
B. 12
C. 6
D. 14
E. None of these
Explanation:
Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 2) + (x + 10) = 24
=> 2x + 12 = 24 => x = 6
The fourth number = x + 6 = 6 + 6 = 12.