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- Question
In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:
Options- A. 5.4 m
- B. 4.5 m
- C. 5 m
- D. 6 m
- Correct Answer
- 6 m
ExplanationA : B = 100 : 90.A : C = 100 : 87.
B = B x A = 90 x 100 = 30 . C A C 100 87 29 When B runs 30 m, C runs 29 m.
When B runs 180 m, C runs ❨ 29 x 180 ❩m = 174 m. 30 ∴ B beats C by (180 - 174) m = 6 m.
More questions
- 1. A certain sum becomes ? 600 in a certain time at the rate of 6% simple interest. The same sum amounts to ? 200 at the rate of 1% simple interest in the same duration. Find the sum and time.
Options- A. ? 120 and 662/3 yr
- B. ? 150 and 662/3 yr
- C. ? 130 and 662/3 yr
- D. ? 160 and 662/3 yr Discuss
Correct Answer: ? 120 and 662/3 yr
Explanation:
According to the question.
([P + (P x 6 x T)/100] - [P + (P x 1 x T)/100] = 600 - 200
? 5PT/100 = 400
? PT = 8000
Again, for 6% rate,
SI = PTR/100 = (8000 x 6)/100 = ? 480
? Sum = 600 - 480 = ? 120
As we have, PT = 8000
? T = 8000/120 = 200/3 = 662/3 yr- 2. A can do a work in 15 days. A and B together do the same work in 10 days. If they are paid ? 1500 for the work, how should the money be divided between A and B?
Options- A. 1000, 500
- B. 500, 1000
- C. 750, 750
- D. None of these Discuss
Correct Answer: 1000, 500
Explanation:
- 3. The tank-full of petrol in Arun's motor-cycle lasts for 10 days. If he starts using 25% more everyday, how many days will the tank-full of petrol last?
Options- A. 5
- B. 6
- C. 7
- D. 8 Discuss
Correct Answer: 8
Explanation:
Let us assume that Arun uses N units of petrol everyday. so the amount of of petrol in the tank when it is full will be 10N. If he starts using 25% more petrol everyday. then the units of petrol he now use everyday will be
N(1 + 25/100) = 1.25N
So, the number of days his petrol will now last will be equal to (amount of petrol in tank) / (number of units used everyday)
= (10N) / (1.25N) = 10 / 1.25
= 8 days- 4. Value of ? in expression
78.9 ÷ (343)1.7 x (49)4.8 = 7? is
Options- A. 13.4
- B. 12.8
- C. 11.4
- D. 9.6 Discuss
Correct Answer: 13.4
Explanation:
78.9 ÷ (343)1.7 x (49)4.8 = 7?
Apply the law of Fractional Exponents and Laws of Exponents
(am)(an) = am+n
am÷an=am?n
am/an=am?n
(am)n = amn
78.9 ÷ (343)1.7 x (49)4.8 = 7?
? 78.9 ÷ (73)1.7 x (72)4.8 = 7?
? 78.9 ÷ 75.1 x 79.6 = 7?
? 78.9 - 5.1 + 9.6 = 7?
? 718.5 - 5.1 = 7?
? ? = 13.4- 5. Construct a quadratic equation whose roots have the sum = 6 and product = ?16.
Options- A. x2 - 6x - 16 = 0
- B. x2 + 6x - 16 = 0
- C. x2 - ?3x - 16 = 0
- D. None of these Discuss
Correct Answer: x2 - 6x - 16 = 0
Explanation:
Given that :- sum of the roots = 6
And Product of two roots = -16
The required quadratic equation is x2 ? (sum of the roots) x + (product of the roots) = 0
? x2 - 6x - 16 = 0- 6. ? 6 + ?6 + ?6 +........ is equal to
Options- A. 2
- B. 5
- C. 4
- D. 3 Discuss
Correct Answer: 3
Explanation:
As per the given above question , we have
Let, x = 6 + ?6 + ?6 + ?6 +........
On squaring both sides, we have
x2 = 6 + ?6 + ?6 + ?6 +........
? x2 = 6 + x
? x2 - x - 6 = 0
? x2 - 3x + 2x - 6 = 0
? x( x - 3 ) + 2( x - 3 ) = 0
? ( x - 3 ) ( x + 2 ) = 0
? x = 3 and x ? ?2 because numbers are positive.
Thus , correct answer will be 3 .- 7. If X and Y are two sets such that X ? Y has 18 elements, X has 8 elements, and Y has 15 elements, how many elements does X ? Y have?
Options- A. 5
- B. 7
- C. 9
- D. 11 Discuss
Correct Answer: 5
Explanation:
Given in the question ,
n(X ?Y) = 18, n(X) = 8, n(Y) = 15.
Using the formula
n(X ? Y) = n(X) + n(Y) ? n(X ? Y), we get n(X ? Y) = 8 + 15 ? 18 = 5.- 8. In a group of 50 people, 35 speak Hindi, 25 speak both Hindi and English and all the people speak Hindi or English or both. The number of people who speak English only is:
Options- A. 40
- B. 20
- C. 15
- D. 10 Discuss
Correct Answer: 10
Explanation:
Draw a figure and calculate.
Number of people speak English only
= 50 ? (10 + 25)
= 15- 9. If U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11},
A = {2, 4, 7},
B = {3, 5, 7, 9, 11} and
C = {7, 8, 9, 10, 11}.
compute: (A ? U) ? (B ? C)
Options- A. {7}
- B. {9}
- C. {6}
- D. {5} Discuss
Correct Answer: {7}
Explanation:
A ? U = {2, 4, 7} ? {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
A ? U = {2, 4, 7};
B ? C = {3, 5, 7, 9, 11} ? {7, 8, 9, 10, 11}.
B ? C = {3, 5, 7, 8, 9, 10, 11}.
Then (A ? U) ? (B ? C) = {2, 4, 7,} ? {3, 5, 7, 8, 9, 10, 11}
(A ? U) ? (B ? C) = {7}.- 10. Solve the below equation.
173.5 x 177.3 ÷ 174.2 = 17?
Options- A. 8.4
- B. 8
- C. 6.6
- D. 6.4 Discuss
Correct Answer: 6.6
Explanation:
173.5 x 177.3 ÷ 174.2 = 17?
Apply the Laws of Exponents ::
(am) x (an) = am+n
Fractional Exponents ::
am÷ a n=am?n
? 173.5 + 7.3 - 4.2 = 17?
? 176.6 = 17?
? ? = 6.6
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