Question

1. The ratio of two numbers is 7:9. If
each number is decreased by 30,
the ratio becomes 5:7, then the
numbers are :
(a) 210 and 270 (b) 56 and 22
(c) 63 and 81 (d) 105 and 135​

Answer 1

Solution :

The ratio of two numbers originally is 7:9 .

Let the numbers be 7x and 9x respectively .

Now , when each number is decreased by 30, the new ratio becomes 5 : 7.

So

7x - 30 : 9x - 30 = 5 : 7

> [ 7x - 30 ]/[ 9x - 30] = 5/7

> 5[ 9x - 30 ] = 7[ 7x - 30]

> 45x - 150 = 49x - 210

> 4x = 60

> x = 15.

First number - 7x > 105

Second number - 9x > 135

Hence , option D is correct .

This is the required answer .

___________________________________

Answer 2

${\large{\pmb{\sf{\underline{About \; question...}}}}}$

★ Correct question: This question says that the ratio of two numbers is 7:9. If each number is decreased by 30, the ratio becomes 5:7, then the numbers are:

(a) 210 and 270 (b) 56 and 22 (c) 63 and 81 (d) 105 and 135

${\large{\pmb{\sf{\underline{Given \; that...}}}}}$

★ The ratio of two numbers is 7:9

★ Each number is decreased by 30

★ The new ratio becomes 5:7

${\large{\pmb{\sf{\underline{To \; find...}}}}}$

★ The numbers

${\large{\pmb{\sf{\underline{Helping \; Options...}}}}}$

(a) 210 and 270

(b) 56 and 22

(c) 63 and 81

(d) 105 and 135

${\large{\pmb{\sf{\underline{Solution...}}}}}$

★ The numbers = 105 and 135

${\large{\pmb{\sf{\underline{Using \; concepts...}}}}}$

★ Proportions.

${\large{\pmb{\sf{\underline{Assumptions...}}}}}$

★ Let the numbers be 7a and 9a respectively according to the given ratio(7:9)

${\large{\pmb{\sf{\underline{Full \; Solution...}}}}}$

~ As it's already given that the ratio of two numbers is 7:9. And also we already assume 7a and 9a respectively according to the given ratio(7:9)

~ It is already given that each number is decreased by 30, the ratio becomes 5:7. Henceforth,

»»» 7a-30 : 9a-30 = 5:7

»»» (7a-30)/(9a-30) = 5/7

• Let us cross multiply.

»»» 5(9a-30) = 7(7a-30)

»»» 45a - 150 = 49a - 210

• Combining like terms.

»»» 45a - 49a = -210 + 150

»»» -4a = -60

»»» a = -60/-4

»»» a = 60/4

»»» a = 15

• Hence, 15 is the value of a.

~ Now let's find the numbers.

1st number -:

»»» 7a

»»» 7(15)

»»» 7 × 15

»»» 105

• Henceforth, 105 is first number.

2nd number -:

»»» 9a

»»» 9(15)

»»» 9×15

»»» 135

• Henceforth, 135 is second number.

Henceforth, the numbers are 105 and 135 that why option (d) is correct.