Question

The ratio of cost of two articles was 13:15.4 years later when the cost of the first had risen by Rs. 14
and that of the second by 10%, the ratio of their cost become 14. 11, what is their original cost?​

Answer 1

Given:

The initial ratio of the numbers= 13:15

The final ratio = 14:11

Cost of first article is raised by Rs. 14

The cost of second article is raised by 10%.

To find:

The original cost of the articles.

Solution:

Let the original numbers be 13x and 15x.

Cost of first article is raised by Rs. 14.

Let the final cost be 14y and 11y.

13x + 14 = 14y- equation 1

15x + 10% of 15x = 11y

15x + 1.5x = 11y

16.5x = 11y

y = 16.5x /11

Put this value in equation 1:

13x + 14 = 14*16.5x/11

13x + 14 = 21x

21x- 13x = 14

8x = 14

x = 14/ 8

x = 1.75

Cost of first article = 13x = Rs. 22.75

Cost of second article = Rs. 26.25

Therefore the original cost of articles is Rs. 22.75 and Rs. 26.25.

Answer 2

SOLUTION

GIVEN

• The ratio of cost of two articles was 13 : 15

• 4 years later when the cost of the first had risen by Rs. 14 and that of the second by 10%

• The ratio of their cost become 14 : 11

TO DETERMINE

The original cost

EVALUATION

Here it is given that the ratio of cost of two articles was 13 : 15

Let first article cost Rs. 13x and second article costs Rs. 15x

Now it is stated that 4 years later when the cost of the first had risen by Rs. 14 and that of the second by 10%

So the cost of first article becomes

= Rs. ( 13x + 14 )

The cost of second article becomes

$\displaystyle \sf{ = Rs. \: \: 15x \: \times \: \frac{110}{100} }$

$\displaystyle \sf{ = Rs. \: \: 16.5x }$

So by the given condition

$\displaystyle \sf{(13x + 14): \: 16.5x = 14 : 11}$

$\displaystyle \sf{ \implies \: \frac{13x + 14}{16.5x} = \frac{14}{11} }$

$\displaystyle \sf{ \implies \: 231x = 143x + 154 }$

$\displaystyle \sf{ \implies \: 88x = 154 }$

$\displaystyle \sf{ \implies \: x = 1.75 }$

Hence

Original cost of first article

= Rs. ( 13 × 1.75 )

= Rs. 22.75

Original cost of second article

= Rs. ( 15 × 1.75 )

= Rs. 26.25

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