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In a three digit number the digit in the unit’s place is twice the digit in the ten’s place and 1.5 times the digit in the hundred’s place. If the sum of all the three digits of the number is 13, what is the number?
100a + 10b + c
c = 2b → b = c/2
c = 1.5a → a = c/1.5
c/1.5 + c/2 + c = 13
6.5c = 39
c = 6, b = 3, a = 4 ⇒ 436
In a two digit positive number, the digit at the units place is equal to the square of the digit in ten’s place and the difference between the number and the number obtained by interchanging the digits is 54. What is 40% of the original number?
Let the number be 10x + y
And y = x²
10x + y – (10y + x) = 54
9x – 9y = 54
x – y = 6
x² x + 6 = 0
x = 2, 3
y = 4, 9
So the no is 39
39*40/100 = 15.6
If the positions of the digits of a two digit number are interchanged, the number obtained is smaller than the original number by 27. If the digits of the number are in the ratio of 1:2, what is the original number?
original number – 10x + y
(10x + y) – (10y + x) = 27
9(x – y) = 27
x – y = 3
y/x = 1/2
x = 2y
y = 3, x = 6 →63
A certain number of two digits is three times the sum of its digits. If 45 is added to it, the digits are reversed. The number is _______
A certain number of two digits is three times the sum of its digits only 27 satisfies this condition.
27 + 45 = 72
Therefore Ans is – 27
The number obtained by interchanging the two digits of a two digit number is less than the original number by 27. If the difference between the two digits of the number is 3, then what is the original number?
original number – 10x + y
(10x + y) – (10y + x) = 27
9(x – y) = 27
x – y = 3
All the given options not follow the condition.
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 larger number?
2x + 3y = 100 –(i)
3x + 2y = 120 –(ii)
By Solving eqn (i) and (ii)
x = 32, y = 12
The sum of two even numbers is six more than twice of the smaller number. If the difference between these two numbers is 6, If the larger number lies between 15 to 25 Which is the smaller number?
If 12 is smaller number then larger number is 18
Sum =(12+18)=30
Twice of the smaller number = 24.
The sum of two even numbers is six more than twice of the smaller number.
Therefore Number 12 satisfy both the conditions.
A number is divided by 2, 3, 4, 5 or 6, reminder in each case is one. But the number is exactly divisible by 7. The number lies between 250 and 350, the sum of digits of the number will be
LCM of 2, 3, 4, 5 and 6 is 60
60 * 5 + 1 = 7x
7x = 301
Number – 301 ; The sum of digits of the number = 4
Sum of three consecutive odd numbers & three consecutive even numbers together is 231. Difference between the smallest odd number and the smallest even number is 11. What is the sum of the largest even number and largest odd number?
odd numbers – x2, x, x+2 ; even numbers – y2, y, y+2
3x + 3y = 231
x + y = 77
(y – 2) – (x – 2) = 11
y – x = 11
x = 33, y = 44
sum of the largest even number and odd number = 46 + 35 = 81
Sum of eight consecutive odd numbers is 656. Average of four consecutive even numbers is 87. What is the sum of the largest even number and largest odd number?
odd numbers — x8, x6, x4, x2, x, x+2, x+4, x+6
x8 + x6 + x4 + x2 + x + x+2 + x+4 + x+6 = 656
8x – 8 =656
x = 83
Even numbers — y2, y, y+2, y+4
4y + 4 = 87 * 4
y = 86
sum of the largest even number and odd number = 89 + 90 = 179
The sum of the digits of a twodigit number is 6. If the digits are reversed, the number is decreased by 36. Find the number?
a + b = 6
(10a + b) – (10b +a) = 36, a – b = 4
We get a = 5 and b = 1
So number is 51
If the places of last twodigits of a three digit number are interchanged, a new number greater than the original number by 36 is obtained. What is the difference between the last two digits of that number?
let the number be 100a + 10b + c
(100a + 10b +c) – (100a + 10c +b) = 36
b – c = 4
A number when divided by 837 leaves a remainder of 79. What will be the remainder when the same number is divided by 31?
Number = 837*a + 79
when this number is divided by 31, it leaves remainder of 17 (837 is completely divisible)
The numerator of a rational number is 4 less than the denominator. If the numerator is increased by 15 and denominator is decreased by 4, we get 6. Find the rational number?
let the fraction is (p4)/p
now, (p 4 + 15)/(p4) = 6
we get p = 7
so fraction = 3/7
When a number is added to 20 percent of the second number, we get 150 percent of the second number. Find the ratio between the first and second number?
a + (20/100)*b = (150/100)*b
a:b = 13:10
Two different numbers when divided by same divisor leaves remainder 7 and 9 respectively. When their sum is divided by the same divisor remainder was 4. Find the divisor?
Let first number N1 = D*a + 7
and second number N2 = D*b + 9
N1 + N2 = (a+b)*D + 16
Remainder is 4, so D will be 12
A number gets reduced to its twothird when 24 is subtracted from it. Find oneeighth of the number?
a – 24 = 2a/3
we get a = 72
so oneeighth of the number = 72/8 = 9
Three numbers are in the ratio 4:3:5. If the difference between thrice the third number and the sum of first and second number is 64. Find the difference between the first and third number?
15x – (7x) = 64, we get x = 8
difference between first and third number = 5x – 4x = x = 8
Onefifth of a number when subtracted from one – third of the number gives 24. Find the square of the number.
a/3 – a/5 = 24
a = 180, so square = 32400
25% of a number is 2 times 65% of another number. Find the ratio of the second no to the first number?
(25/100)*a = 2*(65/100)*b
b:a = 5:26
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