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- Question
- There are two numbers such that the sum of twice the first number and thrice the second number is 100 and the sum of thrice the first number and twice the second number is 120. Which is the larger number?
Options- A. 32
- B. 12
- C. 14
- D. 35
- Correct Answer
- 32
ExplanationLet us assume the first number is x and second number is y.
According to question,
sum of twice the first number and thrice the second number is 100.
2x + 3y = 100 ...................(1)
and sum of thrice the first number and twice the second number is 120.
3x + 2y = 120...................(2)
Subtract equation (1) from Equation (2) after multiply 2 with Equation (1) and 3 with Equation (2), we will get.
3(3x + 2y) - 2(2x + 3y) = 3 x 120 - 2 x 100
9x + 6y - 4x - 6y = 360 - 200
5x = 160
x = 32
put the value of x in equation (1)
2 x 32 +3y = 100
3y = 100 - 64
3y = 36
y = 12
The larger Number is 32 . - 1. If (p/q)n - 1 = (q/p)n - 3, then the value of n is
Options- A. 1/2
- B. 7/2
- C. 1
- D. 2 Discuss
- 2. Which of the following statements is true?
Options- A. Every subset of a finite set is finite.
- B. Every subset of an infinite set is infinite.
- C. Every subset of an infinite set is finite.
- D. A proper subset of a finite set is equivalent to the set itself. Discuss
- 3. A bill which being due at the end of 4 years is now worth $ 575, but if it is due in 2 years 6 months, it would now be worth $ 620. The sum of the bill is :
Options- A. $ 695
- B. $ 725
- C. $ 713
- D. None of these Discuss
- 4. If the numerator of a fraction is increased by 200% and the denominator is increased by 200% then resultant fraction is 14/5.What is the original fraction?
Options- A. 4/7
- B. 13/12
- C. 11/12
- D. None of these Discuss
- 5. Which of the following sets is finite?
Options- A. I = { x : x ? Z and x2 ? 2x ? 3 = 0 }
- B. B = The set of natural numbers which are divisible by 2
- C. C = The set of lines passing through a point.
- D. D = { x : x ? Z and x > - 5 } Discuss
- 6. A shopkeeper allows a discount of 10% to his customers and still gains 20%, the marked price of the article which costs ? 450, is
Options- A. ? 600
- B. ? 540
- C. ? 660
- D. ? 580 Discuss
- 7. Which of the following sets is finite?
Options- A. The set of the months of a year
- B. {1, 2, 3,?}
- C. {1, 2, 3,? 90, 100}
- D. The set of lines which are parallel to x-axis Discuss
- 8. A man bought an article listed at ? 1500 with a discount of 20 % offered on the list price . What additional discount must be offered to the man to bring the net price to ? 1104?
Options- A. 8 %
- B. 10 %
- C. 12 %
- D. 15 % Discuss
- 9. In an examination, it is required to get 296 marks out of aggregate marks to pass. A students gets 222 marks and is declared failed by 10% marks . What are the maximum aggregate marks a students can get?
Options- A. 830
- B. 810
- C. 780
- D. 740 Discuss
- 10. 840.003 ÷ 23.999 =?
Options- A. 47
- B. 8
- C. 35
- D. 18 Discuss
More questions
Correct Answer: 2
Explanation:
Given equation is below
(p/q)n - 1 = (q/p)n - 3
Apply the law of Fractional Exponents and Laws of Exponents
a - m = 1/a m
or
am = 1/a - m
(p/q)n - 1 = (q) - (n - 3) x 1/ (p) - (n - 3)
(p/q)n - 1 = (p) 3 - n x 1/ (q) 3 - n
(p/q)n - 1 = (p/q) 3 - n
if pX = pY then X will be equal to Y. means X = Y;
? n - 1 = 3 - n
? 2n = 4
? n = 2
Correct Answer: Every subset of a finite set is finite.
Explanation:
NA
Correct Answer: $ 713
Explanation:
Correct Answer: None of these
Explanation:
Let us assume the original fraction be x/y.
According to question,
200x/100 / 200y/100 = 14/5
2x/2y = 14/5
?x/y = 14/5
Correct Answer: I = { x : x ? Z and x2 ? 2x ? 3 = 0 }
Explanation:
(a) A = { x : x ? Z and x2 ? 2x ? 3 = 0} = {3, -1}.
? A is a finite set.
(b) B = The set of natural numbers divisible by 2 = { 2, 4, 6, 8, 10,?}.
? B is an infinite set.
(c) Since infinite number of lines pass through a point, C is an infinite set.
(d) D = { -4, -3, -2,?}. Clearly D is an infinite set.
Correct Answer: ? 600
Explanation:
Here, r = 10% and R = 20%
? Required per cent = (r + R)/(100 - r) x 100 %
= [(10 + 20)/(100 - 10)] x 100% = (30 x 100)/90 %
This shows that the marked price of the item is 100/3 % more
than its cost price.
? Marked price of the article = (450 x 400)/300
= ? 600
Correct Answer: The set of the months of a year
Explanation:
NA
Correct Answer: 8 %
Explanation:
? Listed price of an article = ? 1500
? Price after first discount
= 1500 x (1 -20/100) = 1500 x 4/5 = ? 1200
Now, second discount = 1200 - 1104 = ? 96
Hence, required percentage = (96/1200) x 100 % = 8 %
Correct Answer: 740
Explanation:
Let the maximum aggregate marks be N
According to the question,
10% of N = 296 - 222
? N/10 = 74
? N = (74 x 10) = 740
Correct Answer: 35
Explanation:
? = 840.003 ÷ 23.999
Here one number is increased and other is decreased to their nearest whole number
= 840 ÷ 24 = 35
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