Question

6)
The ratio of the costs of two houses is 4:3 and the cost of the second house
4,20,000. Let's find the cost of the first house. If the cost of the first hous
was 70,000 more, then let's find the ratio of their costs.
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Answer 1

Appropriate Question :

The ratio of costs of two houses is 4 : 3. If ,

a] The cost of second house is Rs. 4,20,000 then , find the cost of the first house.

b] The cost of first house is Rs. 70,000 more then , find the ratio of their costs.

Required answer :

Ratio of the cost of two houses = 4 : 3.

Let the cost of the first house be 4x and the second house be 3x.

a] We have the cost of the second house as Rs. 4,20,000.

➙ 3x = 4,20,000

➙ x = (4,20,000)/(3)

➙ x = 1,40,000

Then the cost of the first house is ,

• 4x = 4(1,40,000) = Rs. 5,60,000.

∴ The cost of the first house when the cost of second house is Rs. 4,20,000 is Rs. 5,60,000.

b] We are given that the cost of the first house is Rs. 70,000 more than the original cost of the first house then the new cost of the first house becomes ; Rs. 5,60,000 + Rs. 70,000 = Rs. 6,30,000.

So , the new cost of the first house is 6,30,000.

The ratio of the new cost of the first house to the cost of second house = Rs 6,30,000 : Rs. 4,20,000 = 3 : 2.

∴ The ratio of the new cost of the first house to the cost of second house is 3 : 2.

Answer 2

Given that , The ratio of the costs of two houses is 4:3 and the cost of the second house Rs. 4,20,000 .

Exigency To Find : (a) The cost of the first house (b) The ratio of their costs when the cost of the first house was Rs. 70,000 more

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀¤⠀Finding the cost of first house :

❍ Let's Consider the cost of the two houses be Rs. 4x & Rs. 3x , respectively.

⠀⠀⠀⠀⠀Given that ,

• The cost of the second house 4,20,000.

$\qquad \therefore\sf \:3x \:=\: 4,20,000 \:$

$\qquad \dashrightarrow \sf \:3x \:=\: 4,20,000 \:$

$\qquad \dashrightarrow \sf \:x \:=\: \dfrac{4,20,000}{3} \:$

$\qquad \dashrightarrow \sf \:x \:=\: \cancel {\dfrac{4,20,000}{3}} \:$

$\qquad \dashrightarrow \sf \:x \:=\: 1,40,000 \:$

$\qquad \dashrightarrow \underline {\boxed {\pmb{\frak{\purple { \:x \:=\: Rs.\:1,40,000 }}}}}\:\:\bigstar\:$

Therefore,

• The Cost of First house is 4x = 4 × 1,40,000 = Rs.5,60,000

$\therefore \underline {\sf The \:Cost \:of \:First\:House \:is \:\pmb{\bf 5,60,000} . \:}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀¤ Finding the ratio of their costs when the cost of the first house was Rs. 70,000 more :

As , We know that ,

• The cost of the first house was Rs. 70,000 more then the cost of first house .

$\qquad \therefore\sf \: New\:Cost_{(First \:House \:)} \:=\: 4,20,000 + 70,000 \:$

$\qquad \dashrightarrow \sf \: New\:Cost_{(First \:House \:)} \:=\: 4,20,000 + 70,000 \:$

$\qquad \dashrightarrow \sf \: New\:Cost_{(First \:House \:)} \:=\: Rs.6,30,000 \:$

$\qquad \dashrightarrow \underline {\boxed {\pmb{\frak{\purple { \: New\:Cost_{(First \:House \:)} \:=\: Rs.6,30,000\: }}}}}\:\:\bigstar\:$

Therefore,

• The ratio between the new cost of house and original cost of house will be :

$\qquad \dag\:\:\bigg\lgroup \sf{ New\:Cost_{(First \:House \:)} \::\: Original\:Cost_{(First \:House \:)} }\bigg\rgroup$

⠀⠀⠀⠀⠀Here , New cost of first house is Rs. 5,30,000 and original cost of first house is Rs. 4,20,000

$\qquad \dashrightarrow \sf New\:Cost_{(First \:House \:)} \::\: Original\:Cost_{(First \:House \:)}$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \dashrightarrow \sf New\:Cost_{(First \:House \:)} \::\: Original\:Cost_{(First \:House \:)}$

$\qquad \dashrightarrow \sf 5,60,000\::\: 4,20,000$

$\qquad \dashrightarrow \sf 3\::\: 2$

$\qquad \dashrightarrow \underline {\boxed {\pmb{\frak{\purple { \: Ratio_{(\:Original \:and \: New \:cost \:)}\:=\:3:2 }}}}}\:\:\bigstar\:$

$\qquad \therefore \underline {\sf Hence, \:the \:Ratio\:will \:be \:\pmb{\bf 3 : 2 } . \:}$