Question

Answer the following questions:
* Find a number whose fifth part increased by 30 is equal to its fourth part decreased
by 30.
* The sum of four consecutive integers is 266. What are the integers?
* The sum of three consecutive multiples of 8 is 888. Find the multiples.
* The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than
twice its breadth. What are the length and the breadth of the pool?
* Rs. 13500 are to be distributed among Salma, Kiran and Jenifer in such a way that
Salma gets Rs. 1000 more than Kiran and Jenifer gets Rs. 500 more than Kiran. Find
the money received by Jenifer.
* Sum of the digits of a two-digit number is 11. The given number is less than the
number obtained by interchanging the digits by 9. Find the number.
* The difference between two whole numbers is 66. The ratio of the two numbers is 2
: 5. What are the two numbers?
* The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8
more than the number of girls. What is the total class strength?
* The base of an isosceles triangle is cm. The perimeter of the triangle is 4 cm. What
is the length of either of the remaining equal sides?
* If is subtracted from a number and the difference is multiplied by 4, the result is 5.
What is the number?

Answer 1

First question answer :-

$let \: the \: number \: be \ \: x \\ \frac{1}{5} x - 30 = \frac{1}{4} x - 30 \\ \frac{1}{5} x - \frac{1}{4} x = - 30 - 30 \\ \frac{4x - 5x}{20} = - 60 \\ \frac{ - x}{20} = - 60 \\ x = 60 \times 20 \\x = 120$

Second question answer :-

$let \: those \: integers \: be \: \\ x \ \: \: \: x + 1 \: \: \: \: x + 2 \: \: \: \: x + 3 \: \: \: \: x + 4 \\ sum \: = 266 \\ 266 = x + x + 1 + x + 2 + x + 3 + x + 4 \\ 266 = 5x + 10 \\ 256 = 5x \\ x = 51.2$

Third question answer :-

$perimeter \: = 154 \\ length = 2 + 2 \times bredth \\ perimeter \: of \: rectangle \: = 2(l + b) \\ 154 = 2(2 + 2b + b) \\ \frac{154}{2} = 2 + 3b \\ 77 = 2 + 3b \\ 75 = 3b \\ b = 25$

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