1. The sum of the digits of a two digit number is 7. If the number formed by reversing the digits
is less than the original number by 27, find the original number.
2. Divide 28 into two parts in such a way that 6/5 of one part is equal to 2/3 of the other.
3. A number is divided into two parts, such that one part is 10 more than the other. If the two
parts are in the ratio 5 : 3, find the number and the two parts.
4. The cost of two tables and three chairs is ₹705. If the table costs ₹40 more than the chair, find
the cost of the table and the chair.
5. The digits of a 2-digit number differ by 5. If the digits are interchanged and the resulting
number is added to the original number, we get 99. Find the original number.
6. A number consists of two digits whose sum is 5. If we add 9 with the number, the digits in
the number are interchanged.
7. One number is 4 times the other number. If 6 is added to the smaller number and 4 is added to
the larger number, then the later number becomes twice the other number. Find the numbers.
8. A number consisting of two digits becomes 5/6 of itself, if its digits are interchanged. If the
difference of the digits is 1, find the number.
9. Divide 4000 into two parts such that 15% of the first part equals 25% of the second part.
10. In a bus (2x + 5) passengers bought ₹ 50 tickets and (3x – 2) bought ₹ 75 tickets. If the bus
was 48 seater and was just full, find the no. of passengers for each category and collection of
amount for each category .
Answers
7) given:
One number is 4 times of the other number.
If 6 is added to the smaller number and 4 is added to the larger number, then the later number becomes twice the other number.
Smaller number = x
Larger number = y
According to the 1st condition :-
One number is 4 times of the other number.
\implies\sf{y=4x...............(1)}⟹y=4x...............(1)
According to the 2nd conditions :-
If 6 is added to the smaller number and 4 is added to the larger number, then the later number becomes twice the other number.
\implies\sf{y+4=2(x+6)}⟹y+4=2(x+6)
\implies\sf{y+4=2x+12}⟹y+4=2x+12
\implies\sf{4x+4=2x+12\:[Put\:y=4x\: from\:eq(1)]}⟹4x+4=2x+12[Puty=4xfromeq(1)]
\implies\sf{4x-2x=12-4}⟹4x−2x=12−4
\implies\sf{2x=8}⟹2x=8
\implies\sf{x=4}⟹x=4
Therefore,
Smaller number = 4
Now put x = 4 in eq(1) for getting the value of y .
\implies\sf{y=4x}⟹y=4x
\implies\sf{y=4\times\:4}⟹y=4×4
\implies\sf{y=16}⟹y=16
Therefore,
Larger number = 16
Therefore, the two numbers are 16 and 4