Question

The cost of an electrical gadget and the cost of a plumbing material were in the ratio 8:6 last year. This year, each cost was reduced by 4.00 and has changed to 7:5 respectively taking the initial cost of the electrical gadget to be P and that of th plumbing material to be q cal the value of p and q

Answer 1

Given:

The cost of an electrical gadget and the cost of a plumbing material were in the ratio 8:6 last year

This year, each cost was reduced by 4.00 and has changed to 7:5 respectively

Taking the initial cost of the electrical gadget to be P and that of the plumbing material to be q

To find:

The value of p and q

Solution:

We have,

"p" → the initial cost of the electrical gadget

"q" → the initial cost of the plumbing material

The ratio of the cost of the electrical gadget and the plumbing material last year is given as 8:6, so we can form an equation as,

$\frac{p}{q} = \frac{8}{6}$

$\implies p = \frac{8q}{6}$ ..... (i)

Also, this year due to a reduction in each of the cost by 4 the ratio changes to 7:5, so we can form an equation as:

$\frac{p\:-\:4}{q\:-\:4} = \frac{7}{5}$

$\implies 5(p - 4) = 7 (q- 4)$

$\implies 5p - 20 = 7q - 28$

$\implies 5p - 7q = -28 + 20$

$\implies 5 p - 7q = -8$

substituting from (i)

$\implies 5(\frac{8q}{6} ) - 7q = -8$

$\implies (\frac{40q}{6} ) - 7q = -8$

$\implies 40 q - 42q = -48$

$\implies - 2 q = -48$

$\implies q = 24$

Now, substituting the value of q in eq. (i), we get

$p = \frac{8\times 24}{6} = \frac{192}{6} = 32$

Thus,

$\boxed{\bold{The\:value\:of\:p\:is\:\underline{32}}}.\\\\\boxed{\bold{The\:value\:of\:q\:is\:\underline{24}}}.$

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