Question

A box contains 276 coins of 5 rupees, 2 rupees and 1 rupee. The value of each kind of coin is in the ratio 2:3:5 respectively. The number of 2 rupees coin is
(a) 52
(b) 60
(c) 76
(d) 85

Answer 1

Hint: We will first assume the given ratio 2:3:5 in terms of x like 2x, 3x and 5x. Then we calculate the number of coins of different currencies in terms of x and finally we will equate the summation of all the number of coins to 276.

Complete step-by-step answer:
The total number of coins mentioned in the question is 276. And also the value of each kind of coin given is in the ratio 2:3:5.
So now let the value of each kind of coin be 2x, 3x and 5x respectively.
Now number of coins of Rs. 5 \[=\dfrac{2x}{5}.....(1)\]
Number of coins of Rs. 2 \[=\dfrac{3x}{2}.....(2)\]
And the number of coins of Re. 1 \[=5x.....(3)\]
So now from the given details in the question summation of equation (1), equation (2) and equation (3) is equal to the total number of coins that is 276. So using this information we get,
\[\Rightarrow \dfrac{2x}{5}+\dfrac{3x}{2}+5x=276.........(4)\]
Now taking the LCM in equation (4) we get,
\[\Rightarrow \dfrac{4x+15x+50x}{10}=276.........(5)\]
Now cross multiplying the terms on both sides in equation (5) we get,
\[\Rightarrow 4x+15x+50x=276\times 10.........(6)\]
Now adding all the terms in the left hand side of the equation (6) and multiplying the terms in the right hand side of the equation (6) we get,
\[\Rightarrow 69x=2760.........(7)\]
Now isolating x and solving in equation (7) we get,
\[\Rightarrow x=\dfrac{2760}{69}=40.........(8)\]
Now substituting the value of x from equation (8) in equation (2) we get the total number of coins of Rs. 2.
Number of coins of Rs. 2 \[=\dfrac{3\times 40}{2}=60\]. Hence the correct answer is option (b).

Note: Understanding the concept of ratio is the key here and also reading the question to thrice is important. We can make a mistake in a hurry in solving equation (4) by taking the wrong LCM and hence we need to be careful while doing this step.