Question

The ratio of price of geometry box to the calculator is 3:4. The total price of both is Rs.350. If the price of geometry box and calculator are increased by \[\dfrac{1}{3}\text{ and }\dfrac{1}{5}\] respectively of their original price, find the ratio of increased price of the calculator to the price of geometry box.

Answer 1

Hint: As the ratio of the prices are given, we can find out the new prices if the fraction by which it is increased is given. So, if the fraction be p by which the original price is increased, so, the new price equals to \[\text{Original Price + P }\times \text{ Original Price}\] after finding out each, take the ratio of it to find the answer.

Complete step-by-step answer:
So, we were given the ratio as 3:4 of the price of the geometry box to that of the calculator. Hence, we can suppose that the price of a geometry box and calculator is 3x and 4x respectively.
So, the total amount is 350 as given in question, we can write it as a form of equation, where, x is a variable or unknown, \[3x+4x=350\] which can be written as\[7x=350.\] Hence, the value of \[\text{x}=\text{5}0\].
Hence, the price of geometry box will be \[3\times 50\Rightarrow Rs.150\] and that of calculator will be \[4\times 50\Rightarrow Rs.200.\]
Now, it was said that the price of geometry was increased by \[\dfrac{1}{3}\] and calculator by that of \[\dfrac{1}{5}\] of their original price.
As the geometry box's original price was Rs.150 and it was increased by \[\dfrac{1}{3}\] of it's original price. So, its increased or new price will be \[Rs.150+Rs.150\times \dfrac{1}{3}\] as its price was increased by \[\dfrac{1}{3}\] of its original price. Hence, on calculating we get,\[\left( Rs.150+Rs.50 \right)\Rightarrow Rs.200\]
Now, for the calculator, as the calculator's original price was Rs.200 and it is increased by \[\dfrac{1}{5}\] of its original price. So, its increased or new price will be \[Rs.200+Rs.200\times \dfrac{1}{5}\] as its price was increased by \[\dfrac{1}{5}\] of its original price. Hence, on calculating it, we get,\[\left( Rs.200+Rs.40 \right)\Rightarrow Rs.240.\]
So, the new or the increased price of the geometry box is Rs.200 and that of the calculator is Rs.240. Hence, the ratio will be\[\text{2}00:\text{24}0\Rightarrow 5:6\]
Thus, the ratio is 5:6.

Note: We can also do the calculation without converting the given ratio into price. As we supposed, the price of the geometry box and calculator is 3x and 4x. So, we will find the new value in terms of x only. As the price of geometry box was increased by \[\dfrac{1}{3}\] so, the new price of geometry box will be \[\left( 3x+\dfrac{1}{3}\times 3x \right)\Rightarrow \left( 3x+x \right)\Rightarrow 4x\] as the price of calculator was increased by \[\dfrac{1}{5}\] . So, its new price will be\[\left( 4x+\dfrac{1}{5}\times 4x \right)\Rightarrow \left( 4x+0.8x \right)\Rightarrow 4.8x\]. Then, find the ratio.