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- Question
- If the number obtained on the interchanging the digits of two-digits number is 18 more than the original number and the sum of the digits is 8, then what is the original number?
Options- A. 50
- B. 51
- C. 35
- D. 53
- Correct Answer
- 35
ExplanationMethod 1 to solve the given question.
Lets assume the unit's digit is y and the ten's digit is x. then, the number is 10 x + y.
According to question, after interchanging the digits, the new number is 10y + x.
Then,
New Number - 18 = Original number
10y + x = 10x + y + 18
? 9y - 9x = 18
? y - x = 2 .....................(1)
Again according to question,
Sum of digits of Original Number = 8
x + y = 8 ..............................(2)
Add the equation (1) and (2) , we will get
y - x + x + y = 2 + 8
? 2y = 10
? y = 5
Put the value of Y in equation (2) , we will get
x + 5 = 8
? x = 8 - 5 = 3
Then , the original number = 10x + y
Put the value of x and y and get the original number.
The original number = 10x + y = 10 x 3 + 5 = 30 + 5 = 35
Method 2 to solve the given question.
Given that sum of digits of original number is 8.
Let us assume that unit digit is x , then ten digit will be 8 - x. (since sum of digits is 8.)
Now Original number = 10( 8 - x) + x
After interchanging the digits , the number = 10x + (8 - x) = 9x + 8
According to question.
New number = original number + 18
? 9x + 8 = 10(8 - x) + x + 18
? 9x + 8 = 80 - 10x + x + 18
? 9x + 8 = 98 - 9x
? 9x + 9x = 98 - 8
? 18x = 90
? x = 90/18
? x = 5
The original number = 10(8 - x) + x = 10(8 - 5) + 5 = 10(3) + 5 = 30 + 5 = 35 - 1. A borrowed sum was paid in the two annual installments of ? 121 each. If the rate of compound interest is 10% pa, what sum was borrowed?
Options- A. ? 217.80
- B. ? 210
- C. ? 220
- D. ? 200 Discuss
- 2. H.C.F . of 2 3, 3 2 and 15 is?
Options- A. 23
- B. 32
- C. 1
- D. 360 Discuss
- 3. 6 children and 2 men complete a certain piece of work in 6 days. Each child takes twice the time taken by a man to finish the work. In how many days will 5 men finish the same work?
Options- A. 6
- B. 8
- C. 9
- D. 15 Discuss
- 4. The cost price of an article is ? 800 . After allowing a discount of 10 %, a gain of 12.5 % was made . Then, the marked price of the article is
Options- A. ? 1000
- B. ? 1100
- C. ? 1200
- D. ? 1300 Discuss
- 5. Find the sum of square of first 35 natural numbers.
Options- A. 14910
- B. 15510
- C. 14510
- D. 16510 Discuss
- 6. Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
Options- A. 16 years
- B. 18 years
- C. 28 years
- D. 24.5 years
- E. None of these Discuss
- 7. In a game of 200 points, A can give 40 points to B and 56 points to C. How many points can B give to C?
Options- A. 20 points
- B. 15 points
- C. 10 points
- D. 5 points Discuss
- 8. The age of the father 5 years ago was 5 times the age of his son. At present the father's age is 3 times that of his son . What is the present age of the father?
Options- A. 33 years
- B. 30 years
- C. 45 years
- D. None of these Discuss
- 9. A man, on tour travel first 160 km, at 64 km/hr. and the next 160km at 80km/hr. the average speed for the first 320 km. of the tour is?
Options- A. 35.55km/hr.
- B. 71.11km/hr.
- C. 36km/hr.
- D. 72km/hr. Discuss
- 10. At what rate percent per annum will a sum of money double in 8 yr?
Options- A. 12 %
- B. 12.5 %
- C. 13 %
- D. 15 % Discuss
More questions
Correct Answer: ? 210
Explanation:
According to the question,
Borrowed sum = [121/{1/(1 + 10/100)}] + 121/(1 + 10/100)2
= 121/(11/10) + 121/{(11/10) x (11/10)]
=110 + 100
= ? 210
Correct Answer: 1
Explanation:
Clearly, 1 is the highest common factor of 23, 32, and 15.
Correct Answer: 6
Explanation:
6C + 2M = 6days
36C + 12M = 1 days
Again 1M = 2C
? 36+12X2 = 1 day
60 children can do the work in 1 day
Now, 5 men = 10 children
? 10 children can do the work in 6 days.
Correct Answer: ? 1000
Explanation:
Here, CP = ? 800 , r = 10 % and R = 12.5 %
? Marked price (MP) = CP x (100 + R)/(100 - r)
= 800 x (100 + 12.5)/(100 - 10)
= (800 x 112.5)/90 = ? 1000
Correct Answer: 14910
Explanation:
Sum of the square of first n natural numbers = n(n+1)(2n+1) / 6
Given n = 35
? Required sum = ( 35 x 36 x 71 ) / 6
= 14910
Correct Answer: 24.5 years
Explanation:
Then, Sachin's age = (x - 7) years.
| ∴ | x - 7 | = | 7 |
| x | 9 |
⟹ 9x - 63 = 7x
⟹ 2x = 63
⟹ x = 31.5
Hence, Sachin's age =(x - 7) = 24.5 years.
Correct Answer: 20 points
Explanation:
A : B = 200 : 160
A : C = 200 : 144
? B/C = (B/A) x (A/C) = (160/200) x (200/144)
= 160/144 = 10/9 = 200/180
Hence, B can give C 20 points
Correct Answer: 30 years
Explanation:
Let us assume the present age of father = F year and Son's present age = S years
According to question, 5 years ago,
Father's age = F - 5 and Son's age = S - 5.
According to the question,
The age of the father 5 years ago was 5 times the age of his son.
F - 5 = 5(S - 5)
F - 5 = 5S - 25.....................(1)
At present the father's age is 3 times that of his son.
F = 3S.................................(2)
Put the value of F from equation (2) in equation (1), we will get
? 3S - 5 = 5S - 25
? 25 - 5 = 5S - 3S
? 20 = 2S
? 10 = S
? S = 10.
Put the value of S in Equation (2). we will get,
F = 3S = 3 x 10 = 30
So the present Age of Father = 30.
Correct Answer: 71.11km/hr.
Explanation:
Average speed = 2t1 x t2/( t1 + t2)
= (2x64x80)/(64+80)km
= (2 x 64 x 80 ) / 144 km/hr.
=71.11km/hr.
Correct Answer: 12.5 %
Explanation:
Let Sum = P, Then SI=P
As Amount A = 2 × P
where , P = Principal
Rate R = (100 × SI)/(P × T)
= (100 × P)/(P × 8) %
= 12.5 %
where , SI= Simple Interest
T= Time
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