Question

80. The ratio of the prices of two watches is 17:25. If the price of the first watch is increased by 10%, and that of the second by Rs. 620, the ratio of their prices becomes 1:2. What are the prices of the two watches?

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

The ratio of the prices of two watches is 17:25. If the price of the first watch is increased by 10%, and that of the second by Rs. 620, the ratio of their prices becomes 1:2. What are the prices of the two watches ?

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{\pink{Given}}}}}$

• The ratio of the prices of two watches is 17:25
• If the price of the first watch is increased by 10%, and that of the second by Rs. 620, the ratio of their prices becomes 1:2.

$\Large{\underline{\mathfrak{\bf{\pink{Find}}}}}$

• The prices of the two watches .

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Let,

• Price of first watch = x
• prise of second watch = y

A/c to question,

( The ratio of the prices of two watches is 17:25 )

➠ x : y = 17 : 25

➠ x/y = 17/25

➠ 25x - 17y = 0 .....................(1)

Again,

( If the price of the first watch is increased by 10%, and that of the second by Rs. 620, the ratio of their prices becomes 1:2 )

➠ [ x + ( x × 10/100) ] : [ y+620] = 1:2

➠ ( x + x/10) : (y+620) = 1:2

➠ (11x/10):(y+620) = 1:2

➠ (11x/10)/(y+620) = 1:2

➠ (22x/10) = (y+620)

➠ 22x - 10y = 6200 .................(2)

Multiply by 22 in equ(1) and 25 in equ(2)

• 550x - 374y = 0
• 550x - 250y = 155000

_________________Sub. it

➠ -76y = -1,55,000

➠ y = (-1,55,000)/(-76)

➠ y = [ 1,55,000/76 ]

Keep value of y in equ(1),

➠ 25x - 17 × [ 1,55,000/76] = 0

➠ 25x = 2635000/76

➠ x = 2635000/(76×25)

➠ x = [ 105400/76 ]

$\Large{\underline{\mathfrak{\bf{\pink{Thus}}}}}$

• Value of x = [ 1,05,400/76 ]
• Value of y = [ 1,55,000/76 ]

$\Large{\underline{\underline{\mathfrak{\bf{Answer\:Verification}}}}}$

( The ratio of the prices of two watches is 17:25 )

➠ x/y = 17/25

➠ [ 1,05,400/76]/[ 1,55,000/76 ] = 17/25

➠ (1,05,400)/1,55,000) = 17/25

➠ (1054)/(1550) = 17/25

➠ 17/25 = 17/25

L.H.S. = R.H.S.

That's proved

Answer 2

Given:

The ratio of the prices of two watches is 17:25.

Condition : If the price of the first watch is increased by 10%, and that of the second by Rs. 620.

The ratio of their proces becomes 1:2

To Find:

The price of the two watch = ?

Solution:

Let the price of 1st watch be x

and 2nd watch be y

A/c to question,

( The ratio of the prices of two watches is 17:25 )

➠ x : y = 17 : 25

➠ x/y = 17/25

➠ 25x - 17y = 0 .....................(1)

Again,

( If the price of the first watch is increased by 10%, and that of the second by Rs. 620, the ratio of their prices becomes 1:2 )

➠ [ x + ( x × 10/100) ] : [ y+620] = 1:2

➠ ( x + x/10) : (y+620) = 1:2

➠ (11x/10):(y+620) = 1:2

➠ (11x/10)/(y+620) = 1:2

➠ (22x/10) = (y+620)

➠ 22x - 10y = 6200 .................(2)

Multiply by 22 in equ(1) and 25 in equ(2)

550x - 374y = 0

550x - 250y = 155000

-76y = -1,55,000

➠ y = (-1,55,000)/(-76)

➠ y = [ 1,55,000/76 ]

Keep value of y in equ(1),

➠ 25x - 17 × [ 1,55,000/76] = 0

➠ 25x = 2635000/76

➠ x = 2635000/(76×25)

➠ x = [ 105400/76 ]