Simple Equations

A. 93
B. 39
C. 75
D. 48
E. Either (a) or (b)
Explanation:
Let the two-digit number be 10a + b
a + b = 12 — (1)
If a>b, a – b = 6
If b>a, b – a = 6
If a – b = 6, adding it to equation (1), we get
2a = 18 => a =9
so b = 12 – a = 3
Number would be 93.
if b – a = 6, adding it to the equation (1), we get
2b = 18 => b = 9
a = 12 – b = 3.
Number would be 39.
There fore, Number would be 39 or 93.

A. 1
B. 2
C. 3
D. 4
E. None of these
Explanation:
Let the two-digit number be 10a + b
a = b + 2 — (1)
10a + b = 7(a + b) => a = 2b
Substituting a = 2b in equation (1), we get
2b = b + 2 => b = 2
Hence the units digit is: 2.

A. 4
B. 5
C. 6
D. -4
E. None of these
Explanation:
9 x + x = 13 + 27
10 x = 40 => x = 4

A. -1
B. -2
C. -3
D. -4
E. None of these
Explanation:
19x + 19y + 17 = -19x + 19y – 21
38x = -38 => x = -1

A. Rs.70
B. Rs.75
C. Rs.50
D. Rs.60
E. None of these
Explanation:
2C + 3T = 1300 — (1)
3C + 3T = 1200 — (2)
Subtracting 2nd from 1st, we get
-C + T = 100 => T – C = 100

A. 2/3
B. 3/5
C. 4/7
D. 5/9
E. None of these
Let the numerator and denominator of the fraction be ‘n’ and ‘d’ respectively.
d = 2n – 1
(n + 1)/(d + 1) = 3/5
5n + 5 = 3d + 3
5n + 5 = 3(2n – 1) + 3 => n = 5
d = 2n – 1 => d = 9
Hence the fraction is : 5/9.

A. Rs.849.40
B. Rs.877.40
C. Rs.901.60
D. Rs.815.20
E. None of these
Let the costs of each kg of apples and each kg of rice be Rs.a and Rs.r respectively.
10a = 24r and 6 * 20.50 = 2r
a = 12/5 r and r = 61.5
a = 147.6
Required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5
= 590.4 + 184.5 + 102.5 = Rs.877.40