Question

The value of 36 coins of 10p and 20p is Rs. 6.60. The number of 20p coins is
(a) 16
(b) 20
(c) 30
(d) 32

Answer 1

Hint: To find the number of 20p coins, we have to denote the number of 10p coins as x and the number of 20p coins as y. From the given data, we will get an equation $x+y=36$ and $10x+20y=660$ . We then have to solve these equations for x and y using any method like substitution, elimination, cross multiplication or determinant.

Complete step by step solution:
We are given that the total number of the coins is 36. Let us denote the number of 10p coins as x and the number of 20p coins as y. Hence, we can form an equation of the form
$x+y=36...\left( i \right)$
We are also given that the total cost of 36 coins is Rs. 6.60. Let us convert Rs. 6.60 into Paise.
We know that 1 Rupee is 100 Paise.
$\Rightarrow 1\text{Rs}=100\text{p}$
Therefore, 6.60 Rupees will be 100 Paise multiplied by 6.60.
$\Rightarrow 6.60\text{Rs}=100\text{p}\times \text{6}\text{.60=660p}$
Now, we can form another equation as follows.
$10x+20y=660...\left( ii \right)$
We have to solve for x and y using equations (i) and (ii). Let us use a substitution method.
From equation (i), we can write y as
$y=36-x...\left( iii \right)$
Let us substitute (iii) in equation (ii).
$\Rightarrow 10x+20\left( 36-x \right)=660$
Let us simplify RHS by applying distributive property on the second term.
$\Rightarrow 10x+720-20x=660$
We have to collect the terms in x in LHS and constants in RHS.
$\Rightarrow 10x-20x=660-720$
Let us simplify both sides.
$\Rightarrow -10x=-60$
We can cancel the negative sign on both sides.
$\Rightarrow 10x=60$
Let us take 10 from LHS to RHS.
$\Rightarrow x=\dfrac{60}{10}$
We have to cancel the zero from the numerator and denominator on the RHS.
$\Rightarrow x=6$
We found the value of x. Now, let us substitute this in equation (iii).
$y=36-6=30$

So, the correct answer is “Option c”.

Note: We can also solve the equations using elimination, cross multiplication or determinant. Students must be aware that when they form equations (i) and (ii). They may write equation (i) as $x+y=660$ or equation (ii) as $10x+20y=36$ thus making the whole solution incorrect.