SAT Mathematics - Linear Equation in Two Variables
Exam Duration: 45 Mins Total Questions : 25
A number consists of two digits such that the digit in the ten's place is less by 2 than the digit in the units place.Three times the number added to \(6\over 7\) times the numberobtained by reversing the digits equals 108. The sum of the digits in the number is
- (a)
6
- (b)
7
- (c)
8
- (d)
9
A two digit number is such that the product of the digit is 8. When 18 is added to the number, then the digits are reversed. The number is
- (a)
18
- (b)
24
- (c)
42
- (d)
81
Eighteen years ago, a father was three times as old as his son.Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is
- (a)
54
- (b)
72
- (c)
105
- (d)
108
A person's present age is two fifth of the age of his mother.After 8 years, he will be one-half of the age of his mother.How old is the mother at present?
- (a)
32 year
- (b)
36 years
- (c)
40 years
- (d)
48 years
A and B each has some money. If A gives Rs. 30 to B then B will have twice the money left with A. But, if B gives Rs.10 to Athen A will have thrice as much as is left with B. How much money does each have?
- (a)
62, 34
- (b)
60, 34
- (c)
62, 30
- (d)
none of these
If three times the larger of two numbers is divided by the smaller one, we get 4 as the quotient and 3 as the remainder Also, if seven times the smaller number is divided by the larger one, we get 5 as the quotient and t as the remainder.Find the numbers.
- (a)
20, 18
- (b)
25,17
- (c)
25, 18
- (d)
none of these
If \({1\over2(2x+3y)}+{12\over7(3x-2y)}={1\over2}{7\over (2x+3y)}+{4\over 3x-2y}=2\) then the value of (2x + 3y) is
- (a)
7
- (b)
6
- (c)
\(1\over 7\)
- (d)
none of these
Rs. 1 and Rs. 5 coins are available (as many requireD).
Find the smallest payment which cannot be made by these coins, if not more than 5 coins are allowed.
- (a)
3
- (b)
14
- (c)
12
- (d)
18
Suppose you walk from home to the bus stand at 4 km/hour and immediately return at x km/hour. If the average speed is 6 km/hour, then the value of x is
- (a)
8 km/hr
- (b)
10 krn/hr
- (c)
12 krn /hr
- (d)
none
7 pens and 3 books cost Rs. 1395, while 5 pens and 4 books cost Rs. 1665, find the cost of a pen and that of a book
- (a)
55, 360
- (b)
45,360
- (c)
35,350
- (d)
none of these
The sum of the digits of a two digit number is 12. The number obtained by inter-changing its digits exceeds the given number by 18. Find the number.
- (a)
75
- (b)
77
- (c)
55
- (d)
57
Arvind has Piggy bank. It is full of one-rupee and fifty paise coins. It contains 3 times as many fifty-paise coins as one rupee coins. The total amount of the money in the bank is Rs. 35.How many coins of each kind are there in the bank?
- (a)
14, 42
- (b)
15, 42
- (c)
14, 52
- (d)
none of these
Hamid has three boxes of different fruits. Box A weighs \(2{1\over 2}\) kg more than Box B and Box C weighs \(10{1\over 4}\)kg more than Box B.The total weight of the boxes is \(48{3\over 4}\) How many kgs does Box A weights?
- (a)
\(15{1\over 2}kg\)
- (b)
\(14{1\over 2}kg\)
- (c)
\(13{1\over 2}kg\)
- (d)
none of these
The sum of the numerator and the denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes \(1\over 2\).Find the fraction.
- (a)
\(3\over 7\)
- (b)
\(2\over 7\)
- (c)
\(4\over 7\)
- (d)
\(5\over 7\)
The sum of two numbers is 16 and the sum of their reciprocals is \(1\over3\).Find the numbers
- (a)
11, 4
- (b)
12, 5
- (c)
12, 4
- (d)
none of these
The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers.
- (a)
638 and 372
- (b)
538 and 362
- (c)
628 and 372
- (d)
none of these
Five years ago, A was thrice as old as B and ten years later A shall be twice as old as B. What are the present ages of A and B?
- (a)
30,40
- (b)
20, 50
- (c)
30, 50
- (d)
none of these
A takes 3 hours more than B to walk 30 km. But, if A doubles his pace, he is ahead of B by \(1{1\over2}\)hours. Find their speeds of walking?
- (a)
\(3{1\over 3}\) km/hr, 5km/hr
- (b)
\(2{1\over 3}\) km/hr, 5km/hr
- (c)
\(1{1\over 3}\) km/hr, 5km/hr
- (d)
none of these
90% and 97% pure acid solutions are mixed to obtain 21litres of 95% pure acid solution. Find the quantity of each type of acid to be mixed to form the mixture.
- (a)
5, 15
- (b)
6, 14
- (c)
5, 15
- (d)
none of these
A fraction becomes \({2\over 3}\)when 1 is added to both its numerator and denominator. And, it becomes \(1\over 2\)when 1 is subtracted from both the numerator and denominator. Find the fraction
- (a)
\(2\over 5\)
- (b)
\(3\over 5\)
- (c)
\(1\over 5\)
- (d)
none of these
For what value ofk, the system of equations 2x + ky = 1, 3x - 5y = 7, has no solutions?
- (a)
\(k={-10\over 3}\)
- (b)
\(k={10\over 3}\)
- (c)
\(k={3\over 10}\)
- (d)
none of these
Find the value of a so that the point (3, a) lies on the line represented by 2x - 3y = 5
- (a)
1
- (b)
3
- (c)
1/3
- (d)
-1/3
What is the condition that the lines ax + by = c and lx + my = n are coincident?
- (a)
\({a\over l}={b\over m}={c\over n}\)
- (b)
\({a\over l}={b\over m}\neq{c\over n}\)
- (c)
\({a\over l}\neq{b\over m}\)
- (d)
\({b\over m}\neq{a\over l}\)
Determine the value of c for which the system of linear equations ex + 3y = 3, 12x + cy = 6 has no solution?
- (a)
6
- (b)
-6
- (c)
±6
- (d)
3
A man has only 20-p and 25-p coins in his bag.If he has 100 coins in all, totalling Rs.22.00, how many coins of each kind does be have?
- (a)
60, 40
- (b)
65, 35
- (c)
75, 25
- (d)
none of these
