Page 103 - ICSE Math 7

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6. P could finish of a work in 4 days and Q could finish of the same work in 9 days. They
5 5
worked together for 5 days and then P left. The remaining work was done by Q. Find the time
required by Q to finish the remaining work.
7. X could complete a piece of work in 16 hours and Y could complete the same work in 20 hours.
They worked together for 8 hours and then Y left. Find the time required by X to complete the
remaining work alone.
8. Two taps P and Q can fill a pool in 6 hours and 9 hours respectively. A third tap, R can empty
the pool in 12 hours. How long will it take to fill the pool, if all the three taps are opened
together?

AT A GLANCE

¾ Ratio is the relation between two quantities of the same kind and of the same unit obtained by
dividing one quantity by the other.
¾ A ratio is known as compound ratio of two or more ratios if its antecedent is the product of
antecedents of the given ratios and its consequent is the product of consequents of the given
ratios.
¾ Multiplying ratio or multiplying factor is the ratio by which the original quantity is multiplied
to get the final quantity.
¾ To divide a given quantity ‘A’ in the ratio x : y,

 x   y 
First part =  x +  × A and Second part =  x +  × A



y

y
¾ To divide a given quantity ‘A’ in the ratio x : y : z,
 x   y   z 
First part =  x ++   × A, Second part =  x ++   × A and Third part =  x ++ 
 × A

y
z
z

y
z

y
¾ When two ratios are equal, they are said to be in proportion.
¾ Three quantities are said to be in continued proportion if the ratio between the first and the second
quantity is equal to the ratio between the second and the third quantity.
¾ In unitary method, the value of a unit quantity is obtained to find the value of the required
quantity.
¾ Two quantities are said to be in direct variation if an increase or decrease in one quantity causes
a corresponding increase or decrease in the other quantity.
¾ Two quantities are said to be in inverse variation if an increase or decrease in one quantity causes
a corresponding decrease or increase in the other quantity.
1
¾ One days’s work =
Number of days required to complete the work
1
¾ Number of days required to complete the work =
One day’s work

Work to be done
¾ Time required to do a certain work =
Work done in unit time

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