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case /data -based (4 Marks)

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Question 14 Marks
When Ram Niwas died, he left all his money for his grandchildren, 4 of whom were boys and 3 were girls. In his will he insisted that each grandchild must get equal share of the total amount of ₹$1,12,00,000$.
Q.1. What fraction of the money did the girls receive?
(a) $\frac{3}{4}$$\quad$(b)$\frac{1}{3}$$\quad$(c) $\frac{3}{7}$$\quad$(d) $\frac{3}{8}$
Q.2. What was the share of each child?
(a) ₹12,00,000$\quad$(b) ₹16,00,000$\quad$(c) ₹21,00,000$\quad$(d) ₹24,00,000
Q.3. How much money did the boys receive in total?
(a) ₹48,00,000$\quad$(b) ₹64,00,000$\quad$ (c) ₹56,00,000$\quad$(d) ₹76,00,000
Q.4. If one of the girls did not take her share and the money was divided among the remaining grandchildren, then the fraction of the money received by the boys is
(a) $\frac{1}{3}$$\quad$(b) $\frac{3}{7}$$\quad$(c) $\frac{1}{2}$$\quad$(d) $\frac{2}{3}$
Answer
The total wealth of $₹1,12,00,000$ was to be divided equally among 7 grandchildren of Ram Niwas out of which 3 parts would be given to the girls (as there were 3 girls out of 7 grandchildren).
1. (c): The fraction of the money received by the girls $=\frac{3}{7}$.
2. (b): Share of each child $=₹\left(\frac{1}{7} \times 1,12,00,000\right)=₹16,00,000$.
3. (b): Out of 7 equal parts, 4 parts of the wealth was to be given to the boys.
$\therefore$ fraction of the money received by the boys $=\frac{4}{7}$.
And so, the money received by the boys
$=₹(\frac{4}{7} \times 1,12,00,000)$
$=₹(4 \times 16,00,000)=₹64,00,000$
4. (d): If one of the girls did not take her share, then the money would be distributed equally among the remaining 6 grandchildren out of which 4 parts would be given to the boys.
So, the fraction of the money that the boys will receive then is $\frac{4}{6}=\frac{2}{3}$.
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Question 24 Marks
Karan, an electrician, undertook the wiring job of a building. He bought $8 \frac{1}{3}$ bundles of an electric cable. Each bundle had $184 \frac{4}{5} m$ of cable.
Q.1.  Find the total length of the cable bought by Karan.
(a) 1260 m$\quad$(b) 1540 m$\quad$(c) 1440 m$\quad$(d) 1680 m
Q.2. If the cost of the cable is ₹ $7 \frac{3}{4}$ per metre, find the amount paid by Karan.
(a) ₹11,935$\quad$(b) ₹9985$\quad$(c) ₹10,105$\quad$(d) ₹10.935
Q.3. Karan used $3 \frac{3}{4}$ bundles of cable for wiring in the first floor of the building. What length of the cable was used for the first floor?
(a) 574 m $\quad$(b) 693 m$\quad$(c) 702 m$\quad$(d) 737 m
Q.4. Karan cut a length of $13 \frac{4}{5} m$ from a bundle and divided the remaining cable of this bundle into pieces of length 19 m each. How many pieces of 19 m did he get?
(a) 9$\quad$(b) 10 $\quad$(c) 11$\quad$(d) 12
Answer
1. (b) 1540 m: Total length of the cable purchased $=\left(184 \frac{4}{5} \times 8 \frac{1}{3}\right) m =\left(\frac{924}{5} \times \frac{25}{3}\right) m =1540 m$.
2. (a) ₹11,935: Amount paid by Karan $=₹\left(1540 \times 7 \frac{3}{4}\right)=₹\left(1540 \times \frac{31}{4}\right)=₹ 11,935$.
3. (b) 693 m: Length of the cable used for the first floor $=\left(184 \frac{4}{5} \times 3 \frac{3}{4}\right) m =\left(\frac{924}{5} \times \frac{15}{4}\right) m =693 m$.
4 (a) 9: Remaining length of the cable in the bundle (after cutting a length of $13 \frac{4}{5} m$ )
\[
=\left(184 \frac{4}{5}-13 \frac{4}{5}\right) m=\left(\frac{924}{5}-\frac{69}{5}\right) m=\frac{855}{5} m=171 m.
\]
Number of pieces of length 19 m obtained from the remaining cable $=\frac{171}{19}=9$.
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case /data -based (4 Marks) - MATHS STD 7 Questions - Vidyadip