GATE Mechanical 2020 Set 2 | GA Question: 5

Question

There are five levels $\{P, Q, R, S, T\}$ in a linear supply chain before a product reaches customers, as shown in the figure.

At each of the five levels, the price of the product is increased by $25 \%$. If the product is produced at level $P$ at the cost of Rs. $120$ per unit, what is the price paid (in rupees) by the customers?

• A. $187.50$
• B. $234.38$
• C. $292.96$
• D. $366.21$

Answer 1

Given that, at each of the five levels, the price of the product is increased by $25\%.$

Then, the price paid (in rupees) by the customers

$\qquad = 120 \times \frac{125}{100} \times \frac{125}{100} \times \frac{125}{100} \times \frac{125}{100} \times \frac{125}{100}  = \frac{46875}{128} = 366.21.$

Or

The price paid (in rupees) by the customers $ = (1.25)^{5} \times 120 = 366.21.$

So, the correct answer is $(D).$

Comments

Are we counting customer as a separate level?

Price at level P is 120. If we increase 25% at 5 levels Q, R, S, T and customer level then we will get D as answer. Otherwise if we do not count customer as a separate level then we will get C as answer.

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Yes, in the diagram customer is on a separate level.

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do compounding

Answer 2

The item has already been produced at level P and it will go at level Q. Hence increase in price starts from Q, R, S, T.

= 120( 1+0.25)^4

=292.96

Option C should be the answer

Comments

As mentioned in the question itself: At each of the five levels, price of the product incresed by 25% so there will be 5 in power

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Increased by 25% is 1.25 times of original value

P  to Q increased by = 120*1.25

Q to R increased by again 1.25 so = 120*1.25*1.25 = 120*(1.25)²

R to S increased by again 1.25 so = 120*1.25*1.25*1.25 = 120*(1.25)³

S to T  increased by again 1.25 so = 120*1.25*1.25*1.25*1.25 = 120*(1.25)⁴

T to CUSTOMER increased by again 1.25 so = 120*1.25*1.25*1.25*1.25*1.25 = 120*(1.25)⁵ =366.21

ANSWER = D