Question

Two numbers are in the ratio 17: 45.one third of the smaller is less than 1/5 of the bigger by 15.the smaller is

Answer 1

Let x and y are two numbers where y > x
A/C to question,
x/y = 17/45
⇒ 45x = 17y

Again, one 3rd of samller number = 15 + 1/5 × bigger number
x/3 + 15 = y/5
⇒x/3 - y/5 + 15 = 0
⇒(5x - 3y)/15 + 15 = 0
⇒5x - 3y + 225 = 0
⇒45x - 27y + 225 × 9 = 0 [ multiply with 9 ]
⇒17y - 27y + 2025 = 0
⇒ y = 2025/10
And smaller is x = 17 × 2025/(10 × 45)
x = 17 × 9/2 = 153/2

Hence, answer is 153/2

Answer 2

$\huge{\mathfrak{\underline{Answer :}}} \\ \\ \underline{\boxed{\sf{Smaller \: Number = 76 \frac{1}{2}}}} \\ \\ \sf \huge{\mathfrak{\underline{Step-by-Step \: Explanation :}}} \\ \\ \textsf{Let Smaller Number be 17x.} \\ \textsf{Let Greater Number be 45x.} \\ \\ \sf \underline{ATQ,} \\ \\ \implies \sf 17x \times \frac{1}{3} + 15 = 45x \times \frac{1}{5} \\ \sf \implies 45x \times \frac{1}{5} - 17x \times \frac{1}{3} = 15 \\ \sf \implies 9x - \frac{17x}{3} = 15 \\ \sf \implies \frac{27x - 17x}{3} = 15 \\ \sf \implies \frac{10x}{3} = 15 \\ \sf \implies x = \frac{15 × 3}{10} \\ \sf \implies x = \frac{9}{2} \\ \\ \sf{Smaller \: Number} \\ \qquad \sf = 17x \\ \qquad \sf = 76 \frac{1}{2} \\ \\ \large{\underline{\textbf{Thanks ..!!}}}$