(a) Aditya has a certain number of pencils. The cost of pencils is 10 greater than 4 times the number of pencils which Aditya has. The total cost of the pencils is Rs 162. Frame the equation and find the number of pencils.

(b) People of Sundargram planted a total of 102 trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees was two more than three times the number of fruit trees. What was the number of fruit trees? [4 MARKS]

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Solution

(a) Steps: 1 Mark
Result: 1 Mark
(b) Steps: 1 Mark
Result: 1 Mark

(a) Let Aditya have x pencils

Now 4 times the number of pencils which Aditya has is $4 \times x = 4 x$

10 greater than $4 x = 4 x + 10$

Now, given that the total cost is Rs 162, we get

$(4 x + 10) = 162$

$\Rightarrow 4 x = 162 - 10$
$\Rightarrow 4 x = 152$
$\Rightarrow x = \frac{152}{4}$
$\Rightarrow x = 38$
So, Aditya has 38 pencils.

(b) Total trees planted = 102
Let the number of fruit trees planted be $x$
$∴$ The number of non-fruit trees planted is $3 x + 2$
No. of Non-fruit trees + No. of fruit trees = Total no. of trees
$3 x + 2$ + $x$ = $102$
$4 x + 2 = 102$
$2 x + 1 = 51$
$2 x = 50$
$x = 25$
Therefore no. of fruit trees was 25.

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