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MATHS [3 marks sum]

Unitary Method (Including Time and Work) · ICSE STD 7 (ICSE - English Medium). 5 questions.

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Question 13 Marks
A truck uses 20 litres of diesel for 240 km. How many litres will be needed for 1200 km?
Answer
litres of diesel used for $1 \mathrm{~km}$.
240 km & 20 litres
$ \begin{aligned} & 1 \mathrm{~km}=\frac{20}{240} \text { litres } \\ & =0.0833 \text { litres } \end{aligned} $
litres of diesel used for $1200 \mathrm{~km}$.
$ \begin{aligned} & 1 \mathrm{~km}=0.0833 \text { litres } \\ & 1200 \mathrm{~km}=0.0833 \times 1200 \text { litres } \\ & =99.96 \\ & \approx 100 \text { litres } \end{aligned} $
100 litres of diesel is required for $1200 \mathrm{~km}$.
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Question 23 Marks
In 2 days and 20 hours, a watch gains 20 sec ; find how much time will the watch take to gain 35 sec.?
Answer
2 days 20 hours $=2 \times 24+20=48+20=68$ hours
Now 20 sec. are gained in $=68$ hours
$\therefore 1 \mathrm{sec}$. will be gained in $=\frac{68}{20}$ hours
$35 \mathrm{sec}$. will be gained in $=\frac{68}{20} \times 35$
$=119$ hours $=119 \div 24$ days
$=4$ days 23 hours
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Question 33 Marks
What will be the cost of 3.20 kg of an item, if 3 kg of it costs Rs. 360?
Answer
Cost of $3 \mathrm{~kg}$ of an item = Rs. 360
Cost of $1 \mathrm{~kg}$ of the item $=$ Rs. $\frac{360}{3}$
$\therefore$ Cost of $3.20 \mathrm{~kg}$ of the item $=$ Rs. $\frac{360 \times 3.20}{3}$
$=$ Rs. 384
$\therefore$ Cost of $3.20 \mathrm{~kg}$ of the item $=$ Rs. 384
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Question 43 Marks
If 3 dozen eggs cost Rs. 90, find the cost of 3 scores of eggs. (1 score = 20)
Answer

$ \begin{aligned} & 3 \text { dozen }=3 \times 12=36 \text { eggs, } \\ & 3 \text { scores }=3 \times 20=60 \end{aligned} $
The cost of 36 eggs is $=$ Rs. 90
The cost of 1 egg will be $=$ Rs. $\frac{90}{36}$
$\therefore$ Cost of 60 eggs will be $=$ Rs. $\frac{90 \times 60}{36}$
$ =\text { Rs. } 150 $
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Question 53 Marks
If interest on Rs. 200 be Rs. 25 in a certain time, what will be the interest on Rs 750 for the same time?
Answer
Interest on Rs, 200 is = Rs. 25
$ \text { Interest on Rs, } 1 \text { will be }=\text { Rs. } \frac{25}{200} $
and interest on Rs. 750 will be
$ \begin{aligned} & =\text { Rs. } \frac{25 \times 750}{200} \\ & =\text { Rs. } \frac{750}{8} \\ & =\text { Rs. } 93.75 \end{aligned} $
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