Question

please solve all these sums step by step plzzzzzzzzz!!!!!!

Answer 1

16)
The unit digit of a number is 3 and the number is 7 times the sum of the digits. Find the number
solution:

let two digit number be 10x + y

The unit digit of a number is 3
so, y = 3
then number is 10x + 3

the number is 7 times the sum of the digits
so, 10x + 3 = 7(x+3)
10x + 3 = 7x 21
10x - 7x = 21 - 3
3x = 18
x = 6

so the number is 10*6 + 3 = 60 + 3 = 63

17)
The denominator of a fraction is 9 more than it's numerator. If the numerator and the denominator both are increased by 7, the new fraction becomes 7/10. Find the original fraction.
solution:

let numerator be x and denominator be y

The denominator of a fraction is 9 more than it's numerator
so, y = x + 9

the numerator and the denominator both are increased by 7, the new fraction becomes 7/10
so,
$\frac{(x + 7)}{(y + 7)} = \frac{7}{10} \\ \frac{(x + 7)}{(x + 9 + 7)} = \frac{7}{10} \\ 10(x + 7) = 7(x + 16) \\ 10x + 70 = 7x + 112 \\ 10x - 7x = 112 - 70 \\ 3x = 42 \\ x = \frac{42}{3} \\ x = 14 \\ \\ y = 14 + 9 = 23 \\ \\ the \: original \: fraction \: is \: \frac{x}{y} = \frac{14}{23}$


18)
Raja receive a certain amount of money from his company as bonus . He gives half of the money and additional sum of rupees 10000 to his sister . He also gives one third of the money received and an additional sum of rupees 300 to his brother. If his sister gets twice as much as his brother, find the amount of money Raja received from his company.

solution:

Raja receive a certain amount of money from his company as bonus
so, certain amount be x

He gives half of the money and additional sum of rupees 10000 to his sister
so, he give to his sister = x/2 + 10000......(1)

He also gives one third of the money received and an additional sum of rupees 300 to his brother
so, he give to his brother = (x/3) + 300........(2)

his sister gets twice as much as his brother
so, (x/2) + 10000 = 2((x/3)+300)
(x/2) + 10000 = (2x/3) + 600
10000 - 600 = (2x/3) - (x/2)
9400 = (4x - 3x)/6
x/6 = 9400
x = 9400 * 6
x = 56400

so, Raja received 56400 rupees from his company