Simple Equations

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

A. 74
B. 76
C. 70
D. 68
E. None of these

Explanation:
Let the four consecutive even numbers be 2(x – 2), 2(x – 1), 2x, 2(x + 1)
Their sum = 8x – 4 = 292 => x = 37
Smallest number is: 2(x – 2) = 70.

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.

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.

A. 12 years
B. 21 years
C. 18 years
D. 9 years
E. None of these
Explanation:
Let Mudit’s present age be ‘m’ years.
m + 18 = 3(m – 4)
=> 2m = 30 => m = 15 years.

A. 40
B. 50
C. 60
D. 70
E. None of these
Explanation:
Let the number be
2 + 1/2[1/3(a/5)] = a/15
=> 2 = a/30 => a = 60

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

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.

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

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.