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Denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction ?
A. 5/9
B. 4/7
C. 2/3
D. 3/5d = 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.Cost of 2 chairs and 3 tables is Rs.1300. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by ?
A. Rs.50
B. Rs.60
C. Rs.70
D. Rs.1002C + 3T = 1300 — (1)
3C + 3T = 1200 — (2)
Subtracting 2nd from 1st, we get
-C + T = 100 => T – C = 100Solve the equation for x : 19(x + y) + 17 = 19(-x + y) – 21 ?
A. -3
B. -4
C. -1
D. -219x + 19y + 17 = -19x + 19y – 21
38x = -38 => x = -1Solve the equation for x : 6x – 27 + 3x = 4 + 9 – x ?
A. 2
B. 4
C. 9
D. 129 x + x = 13 + 27
10 x = 40 => x = 4Tens digit of a two-digit number is two more than its unit digit. The two-digit number is 7 times the sum of the digits. Find the units digits ?
A. 0
B. 1
C. 2
D. 5Let 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.Sum of the digits of a two-digit number is 12. The difference of the digits is 6. Find the number ?
A. 39
B. 98
C. 93
D. a and cLet 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.In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number ?
A. 12
B. 18
C. 23
D. 45Let 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.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. 356
B. 134
C. 248
D. 240Let 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) = 240In 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. 864
B. 578
C. 975
D. 975Let 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: 864When 2 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number ?
A. 46
B. 60
C. 21
D. 73Let the number be
2 + 1/2[1/3(a/5)] = a/15
=> 2 = a/30 => a = 60