If the work done by p men in (p + 2) days is to the work done by (p + 4) men in (p − 1) days is in the ratio 1 : 1, then the value of p is

The duration of a railway journey varies as the distance and inversely as the velocity; the velocity varies directly as the square root of the quantity of coal used, and inversely as the number of carriages in the train. In a journey of 50 km in half an hour with 18 carriages, 100 kg of coal is required. How much coal will be consumed in a journey of 42 km in 28 minutes with 16 carriages?

The mass of a circular disc varies as the squares of the radius when the thickness remains the same; it also varies as the thickness when the radius remains the same. Two discs have their thicknesses in the ratio of 16 : 3; find the ratio of the radii if the mass of the first is thrice that of the second.

If p and q are positive integers then √2 always lies between:

The cost of digging a pit was ₹2,694. How much will it cost (approximately) if the wages of workmen per day had been increased by 1/8 of the former wages and length of the working days increased by 1/20 of the former period?

A vessel contains p litres of wine, and another vessel contains q litres of water. r litres are taken out of each vessel and transferred to the other. If r × (p + q) = pq. If A and B are the respective values of the amount of wine contained in the respective containers after this operation, then what can be said about the relationship between A and B?

If sum of the roots and the product of the roots of a quadratic equation S are in the ratio of 3 : 1, then which of the following is true?

The incomes of Rahul, Saurav, and Sachin are in the ratio of 4 : 5 : 6 respectively and their spending are in the ratio of 6 : 7 : 8 respectively. If Rahul saves one fourth his income, then the savings of Rahul, Saurav, and Sachin are in the ratio:

If \( a:b=c:d \), then

\( \dfrac{a}{b}=\dfrac{c}{d} \Rightarrow ad=bc \).

If \( e:f=g:h \), then

\( \dfrac{e}{f}=\dfrac{g}{h} \Rightarrow eh=fg \).

Now consider

\( \dfrac{ae+bf}{ae-bf} \).

Using the proportional relations and simplifying, we obtain

\( \dfrac{ae+bf}{ae-bf}=\dfrac{cg+dh}{cg-dh} \).

X is an alloy of A and B. Y is an alloy containing 80% of A, 4% of B and 16% of C. A fused mass of X and Y is found to contain 74% of A, 16% of B, and 10% of C. The ratio of A to B in X is: